OP why are you hedging so much in your post? Just to be clear:
Your older brother is a paedophile or has committed some sort of child abuse crime, correct? Don't know why you don't just say so instead of hinting heavily. Is it because then it opens up the question of why no-one in your family has taken any action to see him prosecuted?
I have a friend with a family a bit like yours (except they are four daughters so no-one gets off the hook from the insane mother's relentless, narcissistic ways, and the father's total uselessness and detachment). One sister is a drug addict with a personality disorder, lies, steals etc. She lives with the parents and it is totally dysfunctional.
My friend is the family 'victim'. She is expected to sort out all the drama the others create, is constantly on the phone to her mother or to one sister or another about drama with the others. She is taken totally for granted and treated incredibly abusively by the whole family, as everyone takes the cue from the toxic mother. She is totally unable to detach herself from this role as it's all she knows.
I hate watching it, but you can't make someone drop their family any more than you can convince someone to leave an abusive partner - all you can do is support them as best you can until they are ready to make that decision themselves.
As her friend, all I can do is hope when her mother dies it will break the toxic dynamic and she'll finally be able to breathe a bit (although the emotional enmeshment is such I know it will devastate her when her mother does die).
You are quite right to want to keep your baby well away from this gang of nutters. You should do itfor yourself as well, and your partner.
Agree above: look at moving physically away from your toxic family. Set yourself a limit that you will only speak to your mother one hour per day - tell her you will read/listen to all her messages in that hour, then call her to chat for however much time you have left after that in the hour, because you are very busy with work/pregnancy/new baby. Stick to this for a while so she gets used to the fact you are not there for her on tap. Then reduce it. Every other day, then every week.
And boundaries, boundaries, boundaries! Don't tell her anything you're planning to do until it's done - be that a c-section, dying your hair, weaning, booking a holiday, choosing a nursery, anything - and then any post-hoc objections she makes just stonewall with meaningless, emotionless phrases: "I'm sorry you feel that way about it"; "thank you for your advice"; "this is what's right for me/us". Rinse and repeat, rinse and repeat. If she cries, again "I'm sorry that you are upset" (NEVER "I'm sorry I've upset you", you haven't, it's not your responsibility!). If she's mean and nasty, "I don't think this conversation is going well, let's speak about it when you've calmed down" and END THE CONVERSATION, hang up or walk out. REFUSE to be subjected to her nonsense. Her wanting a close relationship with you is not your issue; if she wants it, she needs to earn it.
She may well then try to set your siblings on you, or your dad; luckily it sounds like you have no relationship to speak of with any of them so just straight up ignore them.
Seriously, this relationship is abusive. If she has access to your child (god forbid unsupervised access) she will re-enact this dynamic with them. Do the right thing and protect them.