Are you 55+?
Park Hill is 55+ and is pet free. They have RV sites in their mostly mobile home park. Not sure on availability.
http://parkhillinc.com/wp1/our-park/
Alligator Park also 55+. Allows 2 pets with restrictions.
http://www.alligatorpark.com
Currently parked at Encore Gulf View which is full for JFM...not age restricted and allows pets.
Just here checking things out for the future...I can already see that Punta Gorda is exactly what I am looking for as a snowbird site. It's gonna be 1K month for the peak months but I am ok with that. (And that's if I can get in.)