Family labels

What does everyone think to family labels when you have a baby? I’ve always felt really uneasy with my boyfriends Dad he makes me feel uncomfortable and is quite an obsessive person with everything in general, while I’ve been pregnant he’s been obsessing over babysitting my daughter and going on about it all the time, recently found out that he has been adding young girls on Facebook. I have a 3 month old daughter - how would you Mums deal with this? I think I don’t want him having anything to do with her as I just don’t trust him at all