I had a friend who accidentally discovered, in high school, that her mom and dad were actually her grandparents and her older sister was actually her mom. She had had no idea. She went through a very difficult time after she found out.
Even in an open adoption, the birth parents surrender all parental rights. I was a guardian ad litum in an open adoption. The birth mom and dad had to sign papers surrendering all rights before the adoption could be finalized. I've kept in touch with the adoptive family. They continue to have contact with their daughter's birth mom, but she has no say in how they raise their daughter.
You can give your father guardianship that allows him to make decisions, but if you want to continue to have active legal rights to decisions made about your son, don't allow adoption.
Find someone that can give you legal advice about what will be best for your son and you.