His mother 😡 Please help!

Stephanie
I have been having problems with her since day 1. Her trying to control what I do, telling lies and talking about me behind my back. Causing more problems than anything and trying to insert herself in our lives. Everyone around us is just as annoyed as we are, and they're not even in the situation! Also, I know for a fact that when her 2 year old grandson is in her care, she doesn't take care of him. He recently fell down a flight of stairs while she was supposed to be watching him, and she didn't even get off the couch from watching tv to go get him. 
But now it's worse. When she found out we were expecting, she turns to me and says "I better be seeing a lot of this kid." I just feel like everything she does is invasive and inappropriate. Not only that, but children are not watched and taken care of in her possession (which has been backed up by her own children) leading to accidents and injuries. 
Is it completely unfounded to limit her access to my child, and not leave him/her alone with her? For not only my sanity and my boyfriend's, but for the safety of our baby? Obviously I won't keep her grandchild from her, but she'll be watched like a hawk and have restrictions. 
I cannot have something happen because I knowingly left my child with someone untrustworthy just because that person was its grandmother!Â