agree with moobar and prh47bridge.
forget about the emotional boyfriend/girlfriend bit, keep to the basics that he said he would pay for a holiday, you booked it on his behalf in good faith following his promise to pay for his share of the trip, which he is now refusing to do.
A judge wouldn't order him to pay because of your DD's hurt feelings but you can put your argument plainly that you booked on his behalf with every expectation of being reimbursed. After all, why would you book a holiday for someone without their agreement? The texts between you and his DM are also your evidence in a claim. You have messaged that he owes you and she hasn't denied it, just refused to pay. That's an important distinction.
If you can back your anger off a bit and concede that he can still pay and go on the holiday, you leave him/his parents less room to counter. To the posters saying he'd cause trouble and bring someone back to the accommodation for sex, seriously? I doubt a 19yo on holiday with an exGF and her parents would cause trouble as some posters mention, he'd probably be shitting himself. He can't even deal with this as it is, he's got his mummy to do it for him.
You do seem very angry OP, but try to look past the way he's dumped your DD. They're young, it happens. A two word text or a flowery tearful speech would have the same result of them finishing. It could be a lot worse, at least she's not married to the guy.