It's up to individuals how they choose to parent but fwiw I don't think you sound weird at all op. In fact it amuses me how, in Mumsnet world, young people of 17 who have never left home before, or had a bf or gf before, suddenly morph in to competent adults overnight on their eighteenth birthday. Not all teens are the same. Some will be massively independent and competent at that age and others will be far from that, and a whole load will be somewhere in between.
And as its you, the parents, who would be the ones paying in part for this holiday and mounting any rescue missions (in a global pandemic) should it go wrong, then yes I think it's reasonable that the op has a say in the matter.
The fact they dropped your daughter off in a cab when requested was good (and as I think you realise in hindsight, it would have been better for you to offer to pay for it instead of being impolite yourself op) but I wouldn't want my DD flying off with a mother who, on the only occasion you have met her, was not only drunk, but was seemingly unable to observe any basic niceties. And I think people who are saying they would let their DC fly off with this family having had that experience are being disingenuous.
I do think it's a bit unfair to assume this family are predatory though. Where I come from, families have a tradition of going out together to the pub or what used to be called a working man's club etc (not sure what they are called now or if they still exist). And it's not that unusual on the continent for families to go out for an evening together.
Nor do I think you should necessarily judge the family for not formally asking you for permission for your DD to join them. It may not be usual in their circles to do that, and they may feel they have already been polite and generous enough asking your daughter to go with them. To extend that invitation is a kind thing to do after all.
But most of all, no, your daughter should not be going on holiday during term time and should not be missing her college course. Have you asked her how she is going to justify that to the college and have you made it very clear that you are not going to lie on her behalf? I don't think many schools or colleges would tolerate an absence like that tbh.
I think this is one of those occasions where your daughter may resent you now, but will be - either inwardly or much later on - relieved that you objected. It's far too soon after only 3 months of knowing this lad anyway and his behaviour towards her sounds less than respectful. "No" is a complete sentence. Everyone seems very paranoid on here that saying "no" to your offspring automatically results in a fractured relationship but that's not the case in most families. It's not nice seeing your child unhappy, but most normal parent-child relationships can tolerate a few "no's" here and there.