Advice on mother in law!

Be
Alright, where to start. 
Well first off, she let my 2-year-old nephew fall down the stairs because she wasn't watching him, and then wouldn't get off the couch to go check on him. That's my first problem. 
Now with my kid, who is only two months old, she's already almost dropped him. When she holds him she'll let him throw his head around. Like he had okay head control at this point, he just literally arches and flings himself back and she won't catch him! She came over and just grabbed him away and took him twice when she was very obviously SICK! She knows I don't like her and that I don't like her messing with my son, so she waited until I went out to dinner with my sister in law for her birthday to come over since I wasn't there. Mind you, she tried cancelling on watching her other grandson so that said sister in law could go to her birthday dinner. Just so she could come over when I wasn't there. 
This isn't to mention the emotional trauma and neglect she showed my fiancé, and the rest of her children. 
Am I right for not wanting her around him? It seriously makes me so uncomfortable just for her to hold him now! Even his dad agrees that she won't babysit him whatsoever until he's old enough to watch out for himself (and not fall down stairs).
I just need some MOM thoughts! Is there any happy medium in a situation like this? When I don't even feel like he's safe to be held by her? What to say when she asks to babysit? What to do when she tries to take him since she's constantly sick and won't get vaccinated? She's constantly kissing his face!