No idea about the holiday park, sorry, but I love Sidmouth. It's quite olde worlde with no amusement arcades on the front which is always a bonus!
We spent a fab week there a few years back. The beach is mainly shingle but there is a fab enormous sandy beach just around the headland, a five minute walk, and some fantastic rock pools for your 3 year old.
Just avoid the folk festival week - unless you like that sort of thing - because the place is absolutely mobbed!
I've been there and it's lovely. It is right next to the donkey santuary and just perfect for children. We spent a week there with my nephew. There is a little play area for children and I did not see anything you mention.