It's been a long time but good sitters are hard to come by. If this one is good with your child it would be nice to keep her, but if she's not prepared to operate under your family rules then I think you know what you've got to do. It might just make it all academic anyway if you set limits because she'll likely pack it in if she's going to be forced to watch evil, satanic, demonised kiddie shows.
discreetslave, forgive me please for saying this, but your husband is (edited) mistaken.