IME I think it very much depends on the dog - which only you can know. I very rarely take all 3 these days, but the 10yo lab does get special privileges and always comes, and we never attach him. We know that he’s going to be appropriate - not bark, beg etc. - in fact he’s quite anti-social in that he’s unlikely to approach anyone and just want to sit under the awning or wander around sniffing trees. We find that so long as the dog isn’t causing a problem, and we’re being midful of toileting, people turn a blind eye to the rules. Though of course we do have to face the possibility that might not be the case and we will have to defer to the rules if it upsets anyone at all - and go prepared for it (screw spike and long lead).
Lively dogs aren’t necessarily a problem either, we have a 7yo spaniel x retriever who ONLY wants to play stick ALL DAY, because she doesn’t cause other problems she’s always been well received on campsites as she can keep a large group of children entertained for HOURS when mums and dads are feeling like they’ve woken up too early
In terms of sites I can recommend a couple in Derbyshire where this has never been a problem for us if you like.