I've been bleaching my hair and my friends for years, not a pro but very inclined to get distracted whilst doing it (mine - I do focus when doing friends'!) so I'm used to fixing mess ups!
You need something like Herbatint natural dye, its not damaging to the hair and I've used it before to correct over-bleached hair.
This is very important - do not get a cool toned colour, it has to be warm toned with reddish undertones, something like the 8N colour, warm blonde I think its called.
Also, do not leave it on for the time specified on the box, usually half the time is enough but watch it closely and see, then wash it out when you have the desired colour.
Can you give it at least 48hrs after bleaching before doing it? Or at least as long as you can? Bleaching opens the hair shaft/makes it more porous, so the longer you can leave it the more even and reliable the correction job.
Afterwards use a deep conditioning mask, something like Hask Keratin mask (the pink one, its excellent and cheap) and leave it on for thirty mins.
If you do use a herbal/natural hair colour your DD will ideally have to give it a couple of months before dyeing her hair again, I've done it sooner but the longer you can leave it the better as dyeing over a natural dye gets a little more complicated.