Never been to that part of the country before sorry. Why dont you try using the campsite search facility and narrow it down to your requirements by ticking the boxes on the left. That should give you a few possibilities once you have read the reviews
------------- 2015 Trips
January - Red Squirrel
February - Red Squirrel
March - Gimme Shelter
April - Elie
May - Noah's Ark
May - Riverside, Skipton
May - Blair Castle
June - Braithwaite Bridges
July - The Star
July - Witches Craig
July - Scone
August - Highburn House
September - Gimme Shelter
Personally I prefer sites on the other side of the harbour in the Isle of Purbeck area, but Haven's Rockley Park may be what you're looking for. No tents though, and not sure about dogs.
If you can manage without the entertainment and swimming pool, have a look at Norden Farm - child AND dog friendly!
MERLEY COURT should have most of what you require . Plenty of reviews on here and I have it reviewed in my profile pages . Very close to Poole and major supermarkets .
------------- AussieAl.
Don't forget to leave a review of the campsites you have visited this year or last!