It sounds like your mom is having a power struggle with you.
Maybe it would be in the best interest of you, your mom and your children to find another babysitter. Of course, it may hurt her feelings, but maybe you could tell her that you feel like her tending your children is affecting your relationship and you don't want that to happen.
These are your children. You are the mother and you need to be able to be content with what is being done to take care of your kids. You also don't want to give young children mixed signals. You don't want to have your mom teach them one way and you try another. It's going to mix up the kids.
Maybe there is someone you could ask with the same ideas as you. You can also let your mom know you appreciate her suggestions, but you would like to have things done a different way.
Good luck. I am sure this is a very difficult decision for you.