OP,
Sorry you have had to wade through so many victim blamers, language pendants 🙄.
She sounds horrendous.
Keep your child 100% away from her and hers.
No good will ever come of exposing your child to them
Your mother is doing what she wants to do and that unfortunately includes this awful woman regularly in her house.
I strongly recommend you step away.
You are doing yourselves, your mental health and your family zero favours by listening to your mothers tales of woe anout her.
Step away.
This is like an open sore that is really serving you zero purpose.
Your mother is taking your peace from you by talking to you about it.
You have a very enmeshed relationship with your mum and putting her ahead of whats good for YOU, all the while your mother is outting herself first.
I think you need more counselling to figure this out.
Why are you living your life for your family?
Why haven't you invested in friends and other relationships?
Your mother leans heavily on you, but quickly welcomes back this toxic person into your lives, even if she is your sister.
I think your mother and sister are closer than you think.
You are not making good choices here.
As others have advised, step away, do not visit for a while.
Tell your mother you don't want to hear about her or her drama.
See your mothers partner at your home.
You can invite your mother to your house, on your terms.
It is highly likely your sister will use your mother going forward, so you desperately need to look at your boundaries and protect yourself.
Your mother is giving her priority in her home but quite happy to dump all the drama on you.
This is your life going forward, probably years and years of it ahead of you.
You can tell your mum you love her, and care for her, but going forward you have no wish to be kept informed of the toxic drama of this person.
I repeat, your mother is suiting herself here, it most certainly not your best interests.
Also keep them the hell away from your children.