I think YANBU, entirely.
I'm trying to think back to when I was 17 - I'd started going out with my boyfriend at 16, nearly 17 and had been going out with him for about 3 months when I was invited to go on holiday with him and his father and younger brother. It was pretty intense but we were at school together so had a lot of time together. My parents had met him of course, but not his father (his mother was another kettle of fish entirely and they were long divorced), I don't think but I can't remember exactly! There was certainly no havey caviness about it though, and it's quite likely that they did speak to the BF's father before we went away, but they didn't meet. We only went to the Norfolk Broads though - not fecking Gran Canaria! And iirc, I didn't have to pay except for my own food, because the boat cost the same regardless of whether there were 3 or 4 people on it.
So that was back in the 80s. My parents weren't hippies or totally liberal but they seemed ok with me going to stay with my boyfriend at his dad's house (they never said they weren't, let's put it that way).
However, I had known my BF's family the entire time I'd known him (perils of being at school together, I guess!) so it wasn't like they were strangers to me. Could my parents have refused to let me go? I don't actually know - they didn't try. I was working weekends so had my own money and was going to university after those summer holidays - guess they thought I was big enough to make my own decisions.
So much for my experience of many years ago!
But I don't like your DD's situation much. She met this boy through Twitter, he's already showing dodgy behaviour (the IG thing is very peculiar) and now he and his parents are putting pressure on your DD to comply with their somewhat forward request, instead of being laid back about it. Especially if you are having to pay for her!
I see the red flags but who knows how over-cautious you're being - you're not going to know until/unless something happens/was prevented.
On balance, I would suggest you take a step back and say that you are letting her make her own decision but she needs to fund it herself.