How would you get past this...?

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 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.

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.

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.

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.

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.

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

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.