My SIL and me fell out early on in my relationship with her brother. We are married now, just had our first baby and so excited for the future! But I can really understand how a broken relationship with an inlaw can cause hurt and upset.
I'm kind of both sides of your story... out of the two of us I'm the dramatic one! But I never cause any distress; in fact, no one apart from my DH knows we don't get on! She came to my hen, our wedding and will be invited to the Christening. But, my God, it really does make things awkward! She will have to come visit the baby when we get home and I really just don't want to see her when I'm exhausted and trying to feed!!
It is well managed because we are both adults about it; we had a huge row over something, I will naturally always assume I was right and, understandably, so will she! It was a wound that just never healed and now we just avoid each other or are civil. But sometimes it is just not possible to avoid, I understand that.
It sounds to me like a wound that won't heal and it will hurt you both to force it. The most pressure it put on us was as a couple... my DH is close to my SIL so he often feels compromised which I understand, and I do try terribly hard not to scream "take my side!!!" at him sometimes because I know he can't. I bet you feel the same with your brother...
Family dramas are a given I'm afraid. She is who she is. I feel sad for her because she sounds troubled and that must be hard. I feel sad for you and your concern for your brother and mum. But some things are out of our hands... I hope all works out for the best and you get to spend time with the baby!
If she is awkward about visits... try your absolute hardest to understand pregnancy and birth do crazy things to a woman! Give her space and don't push to visit too soon... I know for me that would make me feel really pressured and want to limit access even more out of avoiding stress for myself. Even though I don't think it's right to restrict access out of spite... see what I mean, I'm on both sides!?!?
Hope for the best outcome for you xxx