I have five DCs who burn easily and I myself burn. We live somewhere sunny and we are all responsible about sun protection. The local community pool gets everyone out of the water every hour on the hour and this has trained them to reapply properly (after drying off) and to get a drink of water (not sugary drinks as these will dehydrate you).
It's up to parents to make sure their own children would sooner come home with a leg missing than come home with a sunburn. It's as important as teaching children to cross the street properly.
I don't think you can be sure your DD applied and reapplied sunscreen since you weren't there and since she ended up burned. I wouldn't be inclined to believe her assurance that she reapplied it.
I agree with the PP^^ who remarked that the British have a 'Grab it while you can because it will be gone tomorrow' attitude to the sun - I am Irish and the Irish have this too.
But still, we all know enough about skin cancer nowadays to put sun protection at the top of our lists of important things to impress upon children. You should have sent her with a rash top since you knew the party was to last five hours. You knew it was the first really hot sunny day of the season just as well as anyone else did.
At 12 your DD should have taken the time to get herself a drink and should have been confident enough to ask to use the loo, and should also have been confident enough to ask someone to help her apply sunscreen in places she couldn't reach. There is nothing cute about shyness that prevents a child from being sensible.
If she couldn't ask where the toilet was, I'd definitely feel I'd failed as a parent.
She was having too much fun to bother getting a drink & applying sunscreen, it happens. She needs to take responsibility & Id take responsibility for not preparing her better for it.
I agree with this point from upthread.
I also agree with the poster (A11) who suggested that a child of 12 who is too shy or lacking in confidence to deal with her own simple needs in a situation where she is with her friends and a friend's parents is in danger while out. There is shy and there is just plain silly. I would tackle this as a matter of urgency, OP. Your DD needs to get over herself, and soon.
I don't blame the hostess for not keeping up with who was applying sunscreen and who wasn't. Even if there had been a break, she might not have noticed a burn developing as the glare of the sun prevents it from being obvious, and also a sunburn gets red in the hours after exposure to the sun ime, not while you are actually getting the damage that will eventually show up as red skin.
The hostess should have provided bottled water in an ice filled cooler, but again, you can lead a horse to water, etc.
I agree with those who suspect the DD plunged into the pool and didn't leave it all day.