Would be rather wary of the teacher taking her through the grades- sounds very unprofessional- and wouldn't be happy anyway because a good grounding in music is v. important. If he has lots of other good qualities (i.e. charismatic teacher, good at engaging her- although obvs. not if she's not concentrating well), then have another go of it. But I'd switch and make a clean break of it.
Good teachers go above and beyond and don't make a fuss about it. They might type up a checklist for practise i.e. all the scales, all the pieces, what the aural entails so the pupil knows exactly what they have to do. They go to seminars (if they're doing ABRSM) and refer to the syllabus regularly. They care about how much you practise at home and recognise the need for structure, especially with beginners. Don't be afraid to ask for a consultation/"probation" lesson which you can sit in on, ask for phone numbers of current pupils, really quiz them. If they're keepers, they'll be glad to tell you about them. It's not a cheap investment and it's best to have one teacher to grow a relationship with, so they've got to be worth it.
To push her confidence up, you could offer her Grade 1 on keyboard. It's not humiliating like a retake (although a retake isn't humiliating, failure is a part of life etc etc and if you're talented at music, it doesn't matter if you get average/below average) because it's on a different instrument, it's slightly easier and she'll know most of it. Chords are fun and useful when it comes to arpeggios later on and she might be attracted to the idea of all the different voice/electronica/rhythms etc. When she gets a good mark on that, she can move on to Grade 2 piano. Trinity Guildhall do keyboard exams.
10-15 minutes a day is good and regular, but you might want to consider making it a little longer. With scales, you just need to slog at them. Learn the first scale and the second, repeat, learn the third scale, repeat them all, then the fourth, repeat them all etc. To get stuck in takes more than 10 mins.
I haven't an ounce of musicality in me, but I somehow I manage to pass exams- mostly merits, but my Grade 5 theory was one mark above the pass cutoff :o v. lucky, I was getting 4/5 marks below in all the practise tests! I only did it so I could take G6, but I wish I'd done it sooner, as soon as I'd started playing. Lots of teachers in France insist on a year of pure theory for all prospective pupils, to test their enthusiasm and to give them a good grounding in music.
My first teacher tried to make everything fun, so neglected theory pretty much completely and gave me the books with the letter names printed next to the notes. When my dad found out he was shocked and switched me to a very theory full-on teacher, who couldn't believe I didn't know what a crotchet was after four years of playing and starting teaching me Grade 3 stuff...I still find it harder to read a bass clef now.
Anyway, do reassure your daughter, especially that it doesn't have to set a precedent.