There's another option........ask for a welfare check from the local law enforcement agency. I'm not saying you can do this everyday, because then they will think you're 'crying wolf'. But if you have any concerns at any time while you know he is there alone...and especially if he calls you with a problem or you try to call him and he doesn't answer.......call and ask for a welfare check. The LEA will go to the residence to see if he's okay.
If this is in a bad neighborhood and there are others in the house that shouldn't be there or there is something else going on that concerns the responding offficer, he/she has the right to take the child out of the home if they feel he is in 'imminent danger'. So when you call, give a contact number and ask them to call you regarding what transpired. If they do have to take him out of the home, make sure the LEA knows you have 50/50 and they can bring the child to your home while they try to get in touch with the mother.
If all this were to happen, then the LEA has an obligation to notify
CPS/DHS and give them a report. It's called 'mandatory reporting' and that's the whole idea behind this.......getting an objective 3rd party to witness what's going on and reporting it. That could force
BM into a corner to comply for the safety of the child.