D.K.
Hi J.,
I'm a ginger and the mom of a ginger so I totally know and feel your daughter's pain! I married into a family that lives at the beach in the summer so have had to adapt. Here's what I have found to work best:
Coppertone has a spray on formula that comes in spf 70, it's in a blue can and is AWESOME! I hate the way sunblock feels on my skin. This stuff is different - you don't have to rub it in, it's more like a laminant. It feels sticky for a minute while it dries then it's like nothing is there. You can find it at Target, Meijer, Wal-Mart, all over the place.
Next, I have learned to put it on all of us first thing in the a.m. before we head out. Then when we get there, about a half hour before we go down to the beach, we reapply. Later, around noon, then again around 2-3. I make the kids stay out a while to let it dry. I know you said reapplying hasn't helped, I can tell you this stuff works, I am a redhead who has stayed all day on the beach & fried then after finding this stuff, I came away without any red, at all. But I think applying early & reapplying is essential.
Have fun!
D.