I actually went to Chessington on the August banknholiday and it was just so busy. There were a lot of very cranky children and parents so not very relaxing. Would you consider a hotel? There is one at the Cotswold Water Park called Four Pillars which offers very good family sized accommodation and often has children eat free offers. The pool is nice for about a 40 minute swim or just for you if you got a chance to use the sauna etc. Nearby is the lovely Cotswold Animal Park and really nearby is a centre with a play park and a nice walk around a lake. I went for three nights one October half term and it felt like a proper holiday.
We're West Sussex and about to head to Isle of Wight over Easter. Short car journey to Portsmouth (an hour for us and we're practically in East Sussex so may be less for you), then a ferry which my DCs are really excited about, and then a short journey to wherever you stay. Lots of stuff to do with children there - both beaches and attractions.
Have a look at Sandy Balls caravan site in the New Forest. It's lovely, a bit like center parcs but on a much smaller scale. It's v popular though so if you want August bank holiday weekend you'll need to book quick. Could combine it with a day trip to Paultons Park or Marwell Zoo. Lovely bike rides through the New Forest too