I'd go with your gut. Sounds like if you keep this family you are going to have problems the whole time as something is always going to bother her as she really does not want to be apart from her child and will probably look for any excuse to pull him out. I'd do a refund and tell her that you really have some reservations about caring for her child and that it is just not going to work out.
If you like family #2 then I would go with them.