Putting Children on Deed

My father has a hand written will leaving everything to my brother and I (his only children). My mother (who passed away in 1973) is still listed on the deed to his house. He wants to have my brother and I listed on the deed. Can we do a quit claim to handle this situation?

An attorney told me we don't need to take my mother's name off the deed as we can use her death certificate. When the time comes, will we end up in probate over this? What's the best way to handle this? We live in New York State.