How would you get past this...?

I wouldn't want anything to do with such people, in fact what they did ( for no reason) sounds a bit nuts.
Life is too short.

Just to reiterate, this person is a close family inlaw.

Just so Fairydoll
However, you cannot treat people the way you have been treated ( with no apology or reason given) and expect them to turn up to an invitation.
However, what you choose to do is up to you, but I can only say what I would do.Good luck.

Could it be that they are offering the invites by way of an apology
Just can't bring themselves to say the actual word.
If there is an estranged child involved then I would consider the invitation.

Other than that I would gracefully decline all future invites.

Consider what you might lose beyond the relationship with this particular inlaw.

If it were me in your shoes, I would be tempted to write once - and once only - to decline the recent invite and say exactly why. I would choose my words carefully - as you have done here - and not trade insult for insult, but still make it plain that their earlier behaviour was unacceptable. Then live with that decision.

I have a family member who has been through something similar. The apparently ' aggrieved' relation, who is a very emotionally needy person has turned the rebuff around so that they are now the 'victim.' I just think you need to put distance down and maintain it. However, only you know if this will compromise other relationships that are impotant to you.

It sounds to me as if they might have realized that they made a mistake/error of judgement, but simply don't have the courage to openly admit this and apologise. They could be naively hoping that you will go along with a pretence that nothing has happened between you.
Obviously, even if that were the case, it wouldn't make your decision on how to respond any easier. Ultimately, only you can decide whether it might be worth going along with such a pretence, whether to ask for an explanation of what has happened, or whether to permanently stay out of their lives. Whatever you decide, I wish you all the best.

I am struggling a bit to understand what went on (although realise that detail might identify them / you)
I would consider having a word with another member of the family who you trust. If that isn't possible, then I think you need to decide how important this relationship is, either to you, or in the life of the child you mention.
If it is important, then accept the invitation, but do not invest any emotion in it. Do what you can to make it work, but don't let yourselves be made to feel bad. If you don't feel it is worth any more of your energy and concern, then decline.

If I were in your shoes I would challenge the behaviour face on . Ask them why they did it and then makes your decision based on the response.

I'm not sure I would be brave enough to do it but my thoughts also were that if it would be useful to maintain this relationship a conversation is needed before accepting any invitations. It doesn't have to be confrontational. Maybe suggest a coffee locally 'to catch up' and explain you were hurt and need to understand. You can then decide if you can put it behind you. Think about the future with and without this person and decide how much contact matters. I hope you can get some peace of mind.

I will not offer advice Fairydoll but you must do what you feel is right for yourself. Similar happened to me with an in law. On the latest occasion I was threatened with the police and never to see the involved children again for no obvious reason except that she was angry with one of my family members. I was distraught for two days and then she contacted me with a request about the children as if nothing had happened. When I met her everything was normal. It seems to me that there are some people on this earth who do not seem to understand how their outbursts can affect others who do not act that way. I honestly believe that confronting her would make the situation infinitely worse and would not change her behaviour at all.

Call me a coward but I ignore the incidents now for the sake of the children and I try to accept that that is 'just the way she is'. I have found out that she has been the same with family and friends all her life.

Life is too short and I no longer waste emotional energy on worrying about it. I hope that you find some way of moving forward.

I would be very chary of going to their house, their home turf, without further investgtion as to the welcome you'll receive. They may well have realised the error of the accusation and being trying to put it behind them and move on. But just as easily you could find yourself cornered by someone trying to justify themselves.

What do the joint offspring think? I assume they'll be there, can the first meeting not be at their house?

I think Nanabilly’s suggestion is the correct one. How you go about that challenge however is important.

If it was me I would ask them to come to my house for a coffee/cup of tea and then tell them how confused you are and ask them, politely, what is going on. This at least will resolve the situation in a ‘kill or cure’ sort of way but at least you’ll have a chance to talk.

I think I would give them one more chance. They have made contact twice. No apology, it is true, but perhaps they realise they were in the wrong. I have a friend who was in a similar situation and who thought the relationship with the in laws was past repair but did accept renewal of contact and now has an amicable relationship even if not best buddies.

You could try and write a very non-confrontational reply that acknowledges what has gone before but tells them that you are prepared to forgive them and move on........

"Thank you for your invitation. I am sure you will remember the letter you sent on xxxx date - we did not reply to it at the time as we were so shocked that you could think such things about us. It is kind of you to invite us to xxxx and we would be happy to come, but, before we accept, we need to be sure that you now understand that you were mistaken about these things that you thought we had done." blah, blah,blah - short and to the point.

Just an idea.

I agree with Imperfect and Luckygirl a letter is the way forward as you need to understand why they said what they did. I would find it difficult to go to their home with this issue unresolved,

Well you have in writing what they thought of you but it seems a bit late to ask for an explanation, obviously you could try if you really want to. We had a similar situation with a slightly more distant relation who upset our DC. We tried a reconciliation after a while as we couldn't believe what had happened but sadly this just bought more problems and we are now estranged. Its a horrible feeling but some people do seem to feel a need to do this. On the charitable side are there any age/mental health problems?

Perhaps you could check who is sending the invitation and if the person who accused you knows about it.

If yes, it is possible that the original letter was written when the person was having some sort of breakdown, or Alzheimers, and got confused, perhaps even meaning it for someone else. Would you know if they have Alzheimers?

Life is too short to bear grudges, it would surely be better for all the other family members and the child in whom you have an interest, if you were all on speaking terms. If it were me I would go, and be civil, and test the water to see if there is any clue as to what caused the person to lash out at you. Maybe there will be an opportunity then, or on a future occasion to have it out, when it is just yourselves and that person present. Obviously the remarks were unforgiveable, but it would help to know what precipitated them.

Nanabilly I think I would do what you suggested but the vague information makes it difficult to say for sure.
Fairydoll2030 I'd be concerned about the mental health of the person who sent the letter so maybe a conversation with his or her closest family member might be a first call?

As they are opening up a channel of communication I would write asking for an explanation of their earlier accusations. Just a single sentence from you is enough.
It may not have been meant for you.

20 years ago i was in pretty similar situation myself with my sister sending me a drunken email rant accusing me of mad things from 50 years ago etc even what we did as children... the shock was enormous / hurtful/ stunning and out of the blue... her explanation she'd pressed the wrong button didn't stop the hurt that she thought and had written down these things...and we corresponded and phoned about it for a while but got nowhere ... I couldn't get over she THOUGHT these things... so i decided to pull back and not see her again unless at family event... i send christmas and birthday cards ... and see her at weddings and funerals where we are civil but don't sit together or exchange news ... just civil .. i don't like the fact i'm no longer in touch with her children .. i miss them growing up ... and i used to be fed up that the wider family didn't know "my"side of the fall out ... i kept my mouth shut and just said... we'd had a falling out... but time has made the split softer and actually ... i no longer care what she thought... nor anything about it now ... it's of no consequence in the grand order of things...
my only dilemma is do i invite her to our 60th wedding anniversary celebrations next summer... emmmm

I like Lucky girls idea ... at least that would clear the air and make her acknowledge her role in all this.

Could the original be an accident meant for someone else - worth considering?

Perhaps the perceived problems have been explained away by another member of the family and they are too embarrassed to apologise?

Try to have the grace to forgive and make a new start with a clean sheet. Everyone would be happier if you could.

I think you need to follow your gut instinct here and do what you feel is right for you. They may have realised their error and are too proud or arrogant to apologise to you properly. You can never unsay or unwrite things that you have done to people, so surely they ar"nt so thick skinned to think that these random invitations will wave a magic wand over it all as if nothing happened. While I would not encourage bearing a grudge against them, I would tread carefully here. Is there another family member you can approach who might be able to shed a bit more light on this situation.

Some people seem to see life as a sort of balance sheet. If they are nasty one day and nice the next, it all balances out so far as they are concerned. If you point out the nastiness they will say 'but what about ...' In their mind you are being unreasonable for bring that up when the latest thing they did was nice.
As others have said, you have to consider the overall impact of any response or lack of response. If there is anyone in the middle who is being affected then it might be better just to rise above it and see how it goes. Otherwise, it is generally better not to have negative or toxic people in your life and if you have nothing to gain by letting them back in your life I wouldn't do it. It is a mistake that I have made and regretted.

OP you say the in law condemnation ran a bus through an important family relationship but you don't say anything about the son or daughter's part in this. Years ago now, the partner of one of my children caused enormous trouble in our relationship with our adult child but she did it partly because of what had been said to her (AC was in counselling) and partly because she was herself very disturbed and had grown up in what would be called a dysfunctional family. I think she enjoyed the fact that what she said and did caused trouble because it isolated our AC from the rest of the family.

So I would concur with those who question the mental health of the person who wrote to you and I'd agree that probably the invitations to dinner are an attempt to make amends. I can't imagine meeting face to face before some attempt has been made to clarify what was going on so I'd agree with those who suggest writing in some way to express your surprise and hurt feelings at the turn of events and to ask for some explanation while also, perhaps, offering olive branches.

If you just accept without any qualification or explanation then you risk things bubbling away under the surface only to recur at a later date.

I imagine you gave limited information for reasons of security, not surprised, but reading your post leaves me wondering what the rest of the story is. One only has to read the estranged thread to know how tangled family relationships can get. All the very best in dealing with this