Not only did your daughter not tell you about the holiday but she's lied to you about how much spending money she actually had available at the time. If you hadn't pushed, your daughter wouldn't have admitted the truth.
Your daughter is very immature, and with the possibility of ADHD/BPD I can understand why you are so worried. She has zero sense of responsibility, incapable of budgeting/looking after her belongings etc.
OP, I would buy decent travel insurance for her and a bottle of sun screen. I would then send her on her way with the £250. I suspect she's fully expecting you to give her further money.
No, she can't afford the holiday, you know it, and so does she really. Once home, she'll need to save for her car insurance again, make it clear, you won't be paying.
Her friends will realise how much support your daughter truly needs, very quickly. If she spends all her money early on and they need to bail her out, I suspect their patience will wear thin. Your daughter is going to have to learn 'friend management' whilst away too. There's no Mum to pick up the pieces.