I'm sorry you're going through this. My Mom was kind of the same way..not to the degree your dad is. She didn't like animals in the house, but that started to change after we got our cat, Pumpkin. She's pretty much an all indoor kitty now and even though my Mom doesn't really approve, she still let's Pumpkin sleep inside and everything.
As for my puppy, my Mom didn't want me to get a puppy. I had been wanting one for 3+ years and when I decided to move out from my roommate's apartment to live on my own, I decided now was the best time. I really needed a little companion. My Mom didn't believe me that I had bought a baby. But I talked to her and told her that I wasn't going to like living alone and I needed a little baby to keep me company. Well, everything worked out well. When my Mom came to visit me in Mexico last year, she bought a little harness for my baby and a dress!
She doesn't like to pet her, but my baby will go and play with her and my Mom will find it funny. She doesn't have a problem with my having my baby in the house or sleeping in my bed. My Mom thinks it's kind of gross but I don't mind.
Good luck to you and your baby. Hang in there.