We were recently at CP Longleat and our accommodation was gorgeous - 3 bed pine lodge. It was hilly but nothing a 4 yr old couldn't happily walk and buggies would be equally easy as the paths are wide and smooth and have wooden pedestrian walkway things over anything remotely steep so that's it more a series of gentle slopes.
If you are not interested in swimming pool I wouldn't bother with somewhere like centreparcs. What is your budget approx? What does the 3 year old like doing and what do the adults like doing? Monmouthshire and Gloucester are both great areas with lots to do, I would second Forest of Dean (though maybe not Clearwell Caves with your age children).
The 3yo is high energy and mainly likes running around or games which involve running around / climbing / throwing things! She quite likes animals too, which is why we thought Longleat might be good, although tbh, she seems less interested in animals if she can’t touch or talk to them iyswim, so don’t know.
DH likes sport, (and sporty games - a bit like dd). I’m more of a quiet walk / bike ride in the woods with picnic type.
Dh and I love food. Dd isn’t fussed, which is why self-catering works well for us.
We’ve been to Bluestone in Wales and we weren’t that into the pool. It was a lot of faff (and quite crowded) for not much entertainment for us. Dd got bored and so did we. So, yes, I think centreparcs might not really be worth it for us right now.
Right I know this might sound mad with a 4 month old...but SIL went here [[ www.penhein.co.uk ]] with a baby & 4 y o and absolutely loved it, we visited her there for a day and the yurt thing did look bloody amazing. Not cheap though.
Sorry just seen not fussed about swimming! There are outdoor play areas and some caves nearby, not far from puzzlewood. Opposite there is a kids railway with little train and lots of outdoor equipment.