Butlins Bognor Regis in the Wave Apartment.
Two grand for a week! 
Never been to Butlins before, but am afraid to fly, so that combined with the Butlins facilities which seem absolutely ideal for two children age 5 and 7 by then, plus lots of undercover stuff in case of rain, make it seem ideal.
I've been to similarly priced Center Parcs (Longleat) before as a couple but can't figure the attraction of it with children, as all activities were extra and there's only so much swimming and walking/cycling in the woods you can do over 7 days. I know thes the zoo next door and a few tourist sites nearby, but as a Wiltshire girl it would be a it of a busman's holiday for me.
Staycations in the UK have surprised me cost wise. I also looked into Bedruthan Steps hotel in Cornwall, but again, had to retrieve jaw from floor at cost.
It's our first ever family holiday, so I am assuming I've booked safely, as the worst possible scenario is bad weather, in which case, there's plenty of indoor activities, plus the children have their own DVDs combo tele in their bedroom and a run of an apartment rather than just