Well, it sounds like she didn't want a baby in the first place, and doesn't want anything to do with him now. She'd be better off giving him up - either to your parents as primary caregivers if thats what they would want, or to adoption. Its unfair that she would use the baby just to get an apartment.

Maybe talk to your parents, if they are concerned about her behaviour around the baby, maybe a nanny-cam of some sort might be a good idea? At least then they might know for sure if she's doing something to make the baby afraid of her.