Your boss is in a very difficult and probably unprofessional position. The hugs and the "baby girl" and "mom" talk have to make her a wee bit uncomfortable. In her position, she probably needs to be careful that she doesn't find herself in over her head. She might already be picking up on the fact that you are very dependent on her. That might be why you feel she isn't as close to you as you would like.

I understand the attachment you feel. I'm just going to encourage you to find other friends, both at work and out in public.

What worries me is, she is older than you. The entire situation makes even me feel a bit uncomfortable. I mean, this could lead down a road that neither of you intend. I hope you are being cautious, and allowing yourself the opportunity to find other friends. Don't make your boss your only friend. Please.