I think you pretty much need to be interviewing for her spot.

She may not want to face the facts but if a doctor has told her that she is allergic to the point where even dander on kids' clothes affect her then how could she even think of leaving her son with you?

She probably loves you and wants to stay and doesn't want to sever ties but maybe you need to be the one to say 'sorry the spot is filled' and give her that push out the door.

I think eventually she will leave or HAVE to leave based on her health - she is just prolonging the inevitable.

Good luck though