Can I be added to the deed/title to my Father's house in Philadelphia, PA. VA Mortgage.

I have lived in & paid the mortgage of my father's home for the last 5 years.

My father has re-married and now lives out of the city. He bought the house before he married, and it was a VA backed mortgage. As far as he is concerned the house is mine, and he no longer has any interest in it.

We want to start some major repairs and my husband and I want some kind of security that if he passes away my step mother will not sell the house from under us. We can not qualify for a mortage on our own at this time.
Can my name can be added to the deed & not cause a penalty or the mortgage due in full.

Or make it so the house is unsellable without my signature? Of course my father is willing to sign whatever papers needed although he does not want to do the leg work.

Please Help!