You MIL sounds awful but your DH needs to take some responsibility for enabling her to treat you (and openly speak about you) that way.
Your BIL sounds horrible too.
I don’t have great in-laws (and that is putting it lightly) and I often wonder how such difficult people produced such a lovely son. 😬
To blatantly not invite you to a “family” event is just nasty. Blaming BIL for not liking you is also nasty. Are these people adults? 🤯
Only you can decide what to do but I have had to dig my heels on more than on occasion with my in-laws and while it caused unpleasantness in the short term, in the long term we have a better understanding and acceptance of each other. That being said, my in-laws were never as overtly nasty as your MIL is. My DH also had to stop choosing to ignore (his way of trying to keep the peace) and had to challenge some of their behaviours, making it clear that it was not acceptable and he would not tolerate it.
If it is a family event DH has to make it explicitly clear, if you are all not invited then no one goes-you are his family. That is on your in-laws if that means they don’t see your DH and DC. That being said, it doesn’t mean you have to go. Politely declining an invitation is fine but not inviting you is awful.
I personally wouldn’t feel comfortable relying on someone like that to provide childcare. It might be harder to get her to be more accepting while she feels like you are indebted to her.
First job is to speak calming to DH and agree steps forward. You need to do damage control before your DC are older.
Good luck and I am sorry you haven’t won the in-law lottery either…I am really envious of people with nice in-laws! I would be happy with easy ones!😬