I want another babysitter besides my mother in law
What's the problem with your mother in law? Is she not supportive?
I feel disconnected from her
It is ok to want a babysitter of your choosing. You should try to repair the relationship with her and make it better.
I don't want to repair it at all. I have no feelings for her.
I think you are allowed to choose who you want to take care of your child. If you think you can't fix things then it is up to you to decide who to babysit your kid. Tell her that she isn't working out to be there for the kids.