It sounds like you've done an enormous amount for her, but got yourself into a bit of a doormat role. I think some good therapy would help you a lot.
That role is probably decades long in the ingraining so you'll struggle to break it, but it's probably the only way you'll get a more healthy role.
I'm very sorry but it sounds to me like your mother takes you utterly for granted and therefore chooses your sister's side over yours, since she is much more independent and she's at less risk of loosing your sister than she is you.
The only person who can change this dynamic is you. Possibly slowly at first by making it clear there are some things you won't do, start with small things.
Sadly, it does not sound possible to ensure a relatinship between your son and his granny. It can't just come from you, it has to be between them, and she is choosing to make it impossible for him to see her.
That's her choice, no matter how she will dress it up and maybe turn it back on you making it yoru fault. it isn't. It's hers. But you are the one who will have to stand tall and act with self respect and not let her mess you and your son around.
A relationship on any terms, being a doormat, is no good relationship at all. Sorry. You can't teach your son to simply give in to everything your neice says or does, which sounds like the only way you can be sure to still see them ... at least until they take umbrage over something else.
You might have to grieve for what should be a much more respectful, caring relationship btw, but isn't.