When I got married, the only people I didn't invite with a plus one were my younger cousins on the grounds that I didn't even know whether most of them had a boyfriend or girlfriend, I certainly hadn't met them if they did, and since they would all be attending with their parents and siblings they wouldn't feel lonely or awkward.
I invited my brother's on-again-off-again girlfriend even though I'm not her biggest fan, because he is my brother and I love him. As it happened, my mum paid for both of their travel costs to my wedding, even though my mum is also not a big fan of the girlfriend. And my brother was 30 at the time, not 18.
Now, if I were getting remarried and I had an 18 year old daughter and it was important to me that she came to the wedding, I would do whatever was necessary to facilitate her attendance, including inviting her boyfriend and paying for her travel, accommodation and food if necessary. I wouldn't expect my ex husband to contribute to the cost of our daughter attending my wedding, that would be ridiculous.
OP's daughter is at an age where she has an almost fully adult way of looking at things, and probably quite a lot of complicated emotions about this wedding, but she doesn't have a job or any real financial independence. It may be that she literally doesn't have enough money to pay for two flights to the UK to attend her father's wedding, plus food and board for the weekend. It may be that she just about has enough money but it would wipe out her savings. Or it may be that she just doesn't want to shell out the equivalent of the cost of a flight to Thailand to travel to the UK for a weekend and watch her father marrying a woman she doesn't particularly like.
Either way, her behaviour is quite understandable and if her father wants to preserve their relationship and have her at his wedding, he should put his hand in his pocket and help her out.
It's not the OP's business or problem though.