But no dog has ever been in Kennels until the first time they are put in kennels!
I think that your best solution would be to book your dog into kennels as close as possible to where you are staying on holiday, and then take your dog out with you during the days when you are off site.
If you will be near the coast, most beaches allow dogs at this time of year, and if your children are still young enough to enjoy making sandcastles, you could all have great fun on a beach, and maybe take a ball and play catch - our dog used to love trying to catch the ball, and running through sandcastles!
If you also take two large flasks away with you, you could have one with tea or coffee in it, and another with hot chocolate, in case you couldn't find a cafe that let's dogs in. From my own childhood I can tell you that in bad weather, car picnics were fun, especially if there was a nice view, and the promise of a (short?) exploration outside whilst well wrapped up and wearing wet weather gear. You may well be aware of my last idea, which is that many of the larger garden centre cafes also allow well behaved dogs in.
But please, whatever you do Do Not take your dog into your caravan. Many of the other guests will be annoyed if they see your dog, and you really do not want to be stood over while you pack up and leave. But the main reason for you not to do it, is that you Will Be incredibly selfish to be willing to risk other peoples health by taking your dog into a dog free caravan. Please believe the PP's when they are saying that a dogs hair or fur is only one thing that can cause allergies! Most animals, including humans and dogs, are constantly shedding dead skin cells, and their saliva and tiny wee and bum drips can frequently cause allergic reactions, and also several very dangerous diseases. The next family in the caravan might have an 8 month old baby crawling on the floor, and a normal caravan clean does not deep wash, or indeed wash at all, a caravans floors. A very quick vacuum is all that the floor gets between guests!
Lastly, please teach your children by example, that breaking the strict rules of places that are providing a service for you, is just as bad as stealing from others, and potentially as nasty as going into the special care unit on a baby ward at a hospital, when you have a streaming cold!