I would either accept her offer to pay for the place and work with her to resolve issue to my standard before allowing child into place or I would terminate.

She been to dr 5 times and still he has, would be wrong diagnosis if same doctor. You sure it different doctors? Who say this? Mom? Can you get permission to speak with the doctor?

To me, if something not makes sense, it not normally true.

Maybe Mom not really understanding what is needed to get rid of these properly.
Maybe family re-infect each other.
Maybe Mom not treating everyone at same time.
Maybe something off with Gary's system for the treatment not be working properly.

I Mom is stating she is doing all she can, then it not enough to reassure you and that fine. Just say that you sorry she has this to deal with but you can't hold the place any longer.