V.W.
I had it in a minor way (on the arms only, not the face or anywhere else) and my kids did too, when they were younger. It was never diagnosed by a doctor because it just wasn't problematic beyond cosmetically. Both my kids had it on the backs of their arms too. Mine came and went... I was self conscious about it wearing tank tops...
Maybe it wasn't even diagnosable KP, but I don't know what else it might have been. :/
Anyway... essentially it is blocked follicles... what I did (can't remember where I read the idea) was apply Selson Blue (yes, the dandruff shampoo) to the backs of my arms and let it sit for a minute before taking my shower. After a few applications it seemed to clear out the clogs and I never have really had it come back. I was probably 23 or 24 yrs old at the time.
I let my son try it a year or so ago (he is 14 now)... His got itchy and he would scratch it. After using the SB a few times, he doesn't really have issues on the backs of his arms anymore either. He did get something like it on his elbows that itched so badly he scratched until it was raw. Dr said it was just dry skin...but it looked just like KP. I let him put SB on that, too. It stung a little, b/c he was scratching it raw so often... but when the skin wasn't raw and he applied it, it did help. It hasn't completely gone away, but it isn't nearly as bad as it was, and he only used it once or twice b/c it stung from the raw from scratching.
My daughter never really wanted to try it (she is 11)... and I won't make an issue of it.
I don't know if it is something you are willing to try or not, particularly since it is on their faces. I would be very hesitant to put anything on their faces. But if your daughter has it elsewhere (her arms?) then you might try putting some on for a few minutes before her bath to see if it helps.
I bought the "old school" one. It is just medicated shampoo, but it has selenium sulfide in it. Be sure to read the label, as some of the varieties don't have that active ingredient in it.
Good luck.