I have read up to about page 7. What is missing for me is the conversation you sat down and had with your daughter when she got a job that paid her £2.60 per hour. For a 35 hour week that works out at £91.00 pw. £394 pcm.
Further up the thread I think you said she also had to pay you £100pcm housekeeping from that and that she had a phone contract for £32 pcm. That leaves the girl with £262 a month. Let's just say she has fares of £3 per day and spends £2.50 a day on lunch and a drink which are reasonable expenses to incur to go to work - that comes to another £110pcm, leaving her with £142pcm.
I think you did absolutely the right thing to pay of the pay day loan by the way - I would do that. I don't think you should have opened her bank statement but I do think you should have confronted her and given her the opportunity to share her problems with you.
Once your dd has paid her day to day expenses she has just over £30 a week for spends and I assume clothes, hair and make-up; that is actually very very little - and that is in return for a full week's work.
She has been silly and immature in her approach to her problems. However, I don't think she necessarily had the support and guidance to keep herself out of trouble in the first place. She is doing an apprenticeship for some experience, she is earning an absolute pittance in return for that experience, if she is going every day and doing her best in a very difficult jobs market I think you should be proud of her and let her know that.
Please draw a line in the sand and move on OP. Please give her some advice and guidance about budgeting in future. Please don't hold this over her - it sounds as though she's doing her best and that she tried to be grown up by trying to sort it out herself even if she did it in the wrong way. Please give her some rope - she hasn't stolen, she hasn't been nasty to you, she hasn't been inconsiderate or even stormed out when you have opened her post and hauled her over the coals.
Our DS is 16 and still at school. He gets about £50 -£60pcm from us, his phone c£25pcm, his lunches and fares paid, his clothes and toiletries paid. At Xmas DH is going to open him a bank account and pay in £125pcm to start teaching him to budget. That will be his monthly spends, toiletries and clothes. We aren't expecting miracles but we will sit down with him beforehand to work out a budget and watch him learn the hard way - hopefully it won't cost us too much and the lesson will be learnt before he goes to university.