He should consult a lawyer. His dog that he has had there for 10 years is far too important to lose arbitrarily. Even if it is legal, which I think it probably is, because a new owner should be able to make the rules for his own park, a lawyer might be able to get them to change their mind, on the basis of the age of the dog, the fact that it has been allowed to live there for 10 years, has lived with your father for all of its life, and it would be too traumatic for your father to have to give his dog away and too traumatic for the dog to have to be re-homed after 10 years. Before your father hires a lawyer, he should go to them and ask about grandfathering in his dog and making the new rule for new people. Perhaps, he can find a way to tug at their hearts. Most people have one, although some are buried amongst a lot of fat.
Certified Paralegal, with 25+ years' experience & with Landlord & Tenant law experience.