Naam, it is not to late to change her. Yes, she may have been spoilt but your dp owes it to her to change it iykwim.
She can't go on throughout her life acting this way every time she doesn't get her own way, when you are a parent it is your job to teach them this. Your dp and dsd's mother need to realise that their dd will not stop loving them if they say "No", she may not like it, she will probably tell them she hates them but at the end of the day she will be thankful for it.
I hung on in there and was strict as I could be with my dd, (of course I made mistakes along the way, teenagers don't come with a handbook) and now she tells me how thankful she is that I did.
There are places that dsd can get councelling over the Summer Holidays try here please don't be put off by the 'mental health' label. They deal with alot of teenagers with emotional problems, CAMHS really helped my dd.
Lol at booking a holiday on your own, it would be pretty boring on your own though, can I come too?
Seriously, you should go on holiday with dsd and dp, you need to show a united front. Dp and yourself should have a long chat with her about what is aceptable behaviour before you go though.