Not sure on the Dorset front but there is a nice static caravan site in Norfolk called "Kelling heath" ~ i went there was i was younger and there's loads of planned forest walks (and little ponds where i saw loads of tadpoles!) and outdoor play centers. They also have indoor centre's with brand new swimming pool complex, gym, onsite shop etc. It is about a 10-15 min drive to the beach if you go to nearby Sherringham or Cromer. We plan to go there next year with our little one (will be about 6 months)
Here's the link: https://www.kellingheath.co.uk/
Another one which is probably abit cheaper would be Haven at Caitor in Great Yarmouth. They have static caravans for 3-5-7 day breaks. I would recommend going for a high end one though and less ones arnt that appealing. They have direct access to the beach and also have a onsite pub, amusement centre, night-time entertainment and is about a 5 min drive to the main town of Great Yarmouth. It was nice a few years ago but its not quite my taste now.
Here's the link: https://www.haven.com/parks/norfolk...gn=Paid_Search-Parks&waGroup=Caister&mpch=sem