Thank god when getting divorced my father did the same for me, now the house was able to stay in the family. Sorry, I know it is not what you want to hear but in ny, it is the only way I could keep it "if" this happened. Which it did.
Robert. You are paying the mortgage on his daughters home. You should have a conversation with all parties involved and discuss these concerns. From there you will be able to decide what the best course of action is.
There are several attorney's in Patchogue that can answer your question. You may want to call Larry Davis, Esq, 631-289-1600. There are a few answers to your question and you should be using an attorney to draft the paperwork.
Unless the house is in both of your names your rights may not be fully protected. If the house was a gift it may be appropriate to put the deed only in her name but if you are using joint assets to pay for the house and/or you are signing for mortgage the fair thing, in my opinion, would be for you and your wife to own the house jointly.
Let Dad Gag on his own property and get a nice place of your own, the guy is trying to crap on you, I assume he does not like you and does this crap thing quite often! If that is the case, tell him shove it and tell him you and his daughter are off for California, okay nnot California, but get your own home free of this guys influence!