Can you tell us more? What was the tutor expecting your DD to do each week? What was the tutor doing in tutorial with her? was it 1-2-1 or class? Did the tutor have a great reputation for getting people in?
I'm asking because there are several issues here. The bleakest scenario is that despite the tutor's best efforts, your DD can't make the grade for a super selective, which Sutton is.
There are plenty more: the tutor wasn't a good fit for your DD and didn't explain in a way that worked for her; the tutor simply wasn't much cop etc.
The main issue now is to build your DD's confidence and techniques in the next six weeks. If it were me, I'd go for 2 hours a day. explain this is a one off and that the rest of the holidays will be spent having fun. Let her choose the hours, and whether she wants to split them or not. Stick to them religiously.
Go over exactly what Sutton requires in exams, in your spare time (I don't know, but check which of VR, NVR, English comprehension/essay, Maths are required. Get hold of the most appropriate books for the school (this forum will have a list somewhere) as well as the how to do it books. Bond has How To Do books, and IPS is self explanatory, explaining as you go along. Spend the first three weeks just looking at relevant material. I'd suggest one hour per day on doing papers, plus one hour per day going over nay mistakes she made, and making sure she understands the processes. Then a week of timed tests, then a week of hardcore revision on weakest subjects, then taper to maybe three papers a week for the final week, or the ten minute a day tests, one in each subject, at 11+ level. If she has to write an essay or story, let us know, and I'll post some pointers, as I teach essay skills.
Give her loads of rewards and small goals to reach. If she concentrates and works hard, reward with a film night or having a friend sleep over, or making pancakes etc. If she gets a certain level of achievement, take her out for an ice cream or swimming or buy her some shiny things from Cl;aire's accessories. Remind her that her work is for her, not you. She is doing it to give herself not only the best chance in life, but the best attitude to life, and even if she fails the exam, that attitude which she has nurtured can't be taken away and will result in higher exam results and better prospects come what may. All the hard work she puts in, whether she passes the exam or not, will always be valuable to her in her life, long term.
As much as she can, help her to enjoy it. Have a giggle about it. Play on Freerice or play scrabble together, or do books of sudoku and wordsearches when you travel on trains. Stuff that is light hearted but keeps her mind alert.
tell her it's only for six weeks and it's worth pulling out the stops.
That said, if she didn't develop with the tutor because she just isn't ready at this level right now, for whatever reason. let her free to enjoy the summer and rave about the local comp. What's most important is that she starts secondary feeling good about her school, her prospects there and herself.