How can I mediate between my brothers?

Mama66, whilst I understand the impulse to “smooth things over”, I would proceed with extreme caution. Any attempt would involve addressing the issues which according to you are SIL. No man worth their salt is going to accept their wife being blamed (rightly or wrongly), and his impulse may be to defend her.
Rather than meddling, maybe just work on having a good relationship with your brothers personally and leave them to sort out any issues they have with each other as adults.

You can't mediate because you are not neutral.

I hope you can see this.

I think you should stay out of the relationship between two adults, and just focus on your own relationship with each of them. They are grown ups who can figure out their own issues. Don’t put yourself in the middle. It’s not your place to mediate.

This must be very hurtful for you, seeing both your beloved brothers so unhappy.

Firstly, as you say, there's no changing your sister in law and that's something you and the younger brother have to accept.

Secondly, the brother married to the lady for 32 years, may be aware she has some emotional or mental issues. This may also be a reason why she wants you all at a distance.

Thirdly, has your elder brother actually said he wants you to mediate? Maybe, for a quiet life, he's happy with this situation. In which case, your 'mediation' may be seen as interference.

If this were me and the brothers would agree, I'd talk separately to them, starting with the elder.

Ask him how he feels about his wife's rejection and if he knows why.
And if he wants you to do something to bring him and his brother closer, as his sibling is so very upset about the whole thing.

You may get a straight, 'No thnaks, we're fine' in which case, that's the answer. Leave it be.

If he says he'd like to be closer to his brother but his wife objects, then suggest they meet privately, without telling her. That's not sneaky, especially if she's emotionally fragile, it's just good practice.

These meetings, perhaps for the occasional lunch, would be on the clear understanding that from respect, his wife is not to be criticied.

This is only to bring the brother closer and criticism will alienate them both.
The younger brother must absolutely agree to this, especially as you all know he'd been wasting his time and upsetting his brother even more.

I hope this works out; they have trusted you to mediate before and maybe will again but it must be their choice.

I don’t think you can or should, they are all adults, I would stay out of it, there are obviously issues here regarding your sil and your brother won’t thank you as it could be seen as meddling in their relationship, nobody knows what goes on behind closed doors, I hope it gets sorted soon x

Maybe she just feels that your family is just too close knit and involved in each others lives and that her family, her husband and children, need some space. Not everyone wants that kind of involvement and actually your not her family. You're a sister and brother of the man she married.

Bear in mind she may not even like either of you. If that sounds harsh we all have to accept that not everybody likes us or would choose our company ?

If you wade in, "putting things right" it will just confirm that feeling she has.

As for the suggestion of arranging for the brothers to meet secretly, effectively deceiving his wife ???

I would just enjoy your own relationship with your brothers, and any relationship you are able to have with your SIL. They are adults and have to sort out their own problems like adults. Do nothing unless they ask for help, and even then be very careful.

I agree with Lolo81 your brothers are adults leave them to sort out their relationship. You can be close to them individually but don't criticise one to the other. Sometimes I'm glad I was an only child, my husband has these sort of issues with his family.

IIIte makes some good points, I’ve just read your post again Op you have been brought up in a loving and close knit family I’m wondering if she is more private and doesn’t want to share certain aspects of her life with other members of the family, you are saying she’s had struggles in her life and we have always tried to be supportive, one persons idea of being supportive could be another persons view of meddling, not saying you have done this as such, can you understand what I mean op, maybe she doesn’t want everything about her life brought out in the open, she’s made it clear you said she wants nothing to do with our side of the family, I think she maybe she finds your close knit family too close

You are also calling your sil a absolute lost cause, Why! Simply cos she’s not like how you are expecting her to be,

Honestly just stay out of it. Agreeing with one is ganging up on the other.

Relationships are a two way street. You have put a lot of pressure on your older brother wanting to know "why" that's probably made things worse. Now your little brother is doing the same. Have you actually been told why and it's just been dismissed because you don't agree?

This is the most important relationship in your older brothers life. The two of you need to stay out of it and focus on having a good relationship with him. He will probably continue to put his wife first and that is how it should be.

I agree with Illte. It's difficult (or impossible?) to mediate "neutrally" when you are a close & caring family member. Stand back.

Just encourage your brothers to respect the SIL's space and suggest they meet up independently, then step back. One of my DIL's doesn't particularly want to spend time with us as a family, especially when we're all together as she doesn't like big groups, and we just extend invitations to the whole family but accept the situation graciously when she has "something else to do."
I certainly would not suggest that there is any dishonesty in meeting up with family members without SIL. You will just give her ammunition to insist that her husband doesn't see you either. Whatever way you look at it, it is a breach of trust.
My SIL was my son's best friend. I think my son has seen a new side to my SIL since he married my daughter which he doesn't like very much (and probably, vice versa) so their relationship has suffered enormously. I think that often happens and it is better to just accept that childhood friendships often don't last.

It’s a really sad situation. I know of many siblings who were once close but are now estranged, myself included. Being one of four children we were always together, but sadly my youngest brother and me haven’t spoken for twelve years. Am I sad? Of course I am but no amount of mediation will ever bring us back together. His wife was the cause. I always thought of her as a sister but unfortunately I found out she had been saying unkind things about me to friends and family. It hurt like hell. My brother naturally stood by his wife and I didn’t expect it to be any other way. It has broken my heart but it’s how it is. I wouldn’t have been happy had either of the other two siblings interfered. Both have now sadly died.
My point is don’t interfere. For me it wouldn’t have helped. It’s how it is. I hope things improve for you. Sending hugs ?

If you mediate, I can guarantee you will lose a relationship with one of your brothers as it looks like you will be taking a side

Let them be. Let them fix this by themselves. They are both adults and they can manage their own problems.

Close knit can easily mean enmeshed to an outsider.

Thank you all for your responses, it really helps to get some outside perspective.

Although it upsets me greatly I think the only course of action is to maintain my relationship with my brothers and nephews and nieces and hope that my brothers sort things out. My older brother does have a tendency to bury his head in the sand about things and my younger brother digs his heels in, so I can’t see things being sorted soon. But I recognise the wisdom in leaving them to it.

As for the person who queried why I described my SIL as a lost cause, I don’t want to be disloyal to her, enough to say I am not saying she is a lost cause lightly.

Thank you once again for your responses.

It's a sad problem for you as we want our family to all get on together, but a mediator should be impartial- you aren't really as you are blaming SIL for the problem.

I agree with those who say stay out of it. I have learnt from experience and initially tried to mediate between my two younger sisters. I found that I became very unhappy and felt sandwiched between the two of them. Now I try and maintain relations separately. Even then I try and be neutral.

You could be a go between but not a mediator - you are too close and have your own agenda. What would the issues be ? That your sister in law isn’t able to fit in ? I suggest you work on your own relationship with your brother and not force the issue. Ps - it takes about 3 years to qualify as a mediator / the term is used very loosely

I would take a step back and stay out of it. Leave them to sort it out themselves if they want to. They are adults after all. I don't get on with my sister and no amount of help from anyone will persuade me to be part of her life. She has been very cutting and nasty and I don't need that in my life.