That's a tough situation. I can completely understand your reservations considering you are living with your parents and, due to this, their reaction is important. Personally, I think finding a way to talk to them about it would be an important first step. Normally I would say otherwise, but since you live under their roof, the situation is a little different.

Unfortunately, it's just not something I've dealt with. Your therapist might be able to give you assistance in how to approach your father regarding your sexual orientation.