Did you ask, and get your answer about charging your car, via email OP, or was it face to face? If by email, then you have proof of what was said, and have a far better case than if you just had a conversation, as then it's a case of, 'he said, she said'.
If you have it in writing, send the site management an email, referring to the email you already have, confirming they said it was OK, and point out your difficulties of charging elsewhere with your children onboard, and say that while obviously if it's a case of 'Health & Safety', you understand, but they do need to provide another suitable charging point. If they won't do that, and you have the previous agreement in writing, then they have broken the contract you have with them, and you would be able to take legal action, or alternatively negotiate selling the caravan, with THEM paying any fees.
However, if it was only ever a spoken agreement, and the person you spoke to is still there, then I would try and speak to them about it, but whatever you do, at least start off by being completely reasonable, not by issuing threats, as that will just get their backs up, and make it far less likely that you will get what you want.