OP, I don't think anybody is obliged to go to a destination wedding, but it seems like that isn't actually what this is about.
You say that money isn't an issue, other than you not wanting to spend five grand on this, it's the fact that you don't want to go to Cyprus and you don't want to spend time with your partner's family. Your partner apparently does want to go.
From the way you are coming across, I do think you are being a little unreasonable.
It's a four and a half hour flight to Cyprus. Easily doable in a long weekend. You could fly out the day before the wedding and back the day afterwards if you didn't want to stay any longer than that. Unless the wedding venue is in the middle of nowhere, there are almost certainly cheaper hotels or even AirBnbs in the local area which you could book instead.
It's still a lot of effort and money for a wedding and if you don't want to go, you don't want to go. And if you can't afford to go, you can't afford to go.
But what is coming across from your posts is that it isn't about the five grand, or it being in the school holidays, or the fact that you've been to Cyprus before. You just don't care enough about your partner's family to want to put yourself out. I suspect you would be on here complaining about it if they were getting married in Cornwall, or in Scotland, or on a Thursday.
If you and your partner have children together (it sounds like you do?) then it probably wouldn't hurt for you to make a bit more effort with his family, unless there is some massive back story here.