I had a whole crop of verruccas for years (and I mean YEARS!) on the ball of one foot. They never hurt me, so I wasn't particularly bothered. However, they started spreading again and reached the side of my foot, where they started hurting (without the pressure of the ball of foot to make them grow inward, they were becoming half verrica, half wart) so I decided to start treating them.
I used the salycilic acid plus a hard skin "buffer" (forgotten the proper word). It was agony, as I was dealing with such a large area, it was as if a whole layer of hard skin on my foot was coming off. I stoppped just before we went skiing, so that my foot had a chance to recover.
Interestingly, although my verrucas were still there, I had managed to get rid of most of the samll ones and the "mummy" and "daddy" ones (ie the original two) were much smaller.
A while later I noticed that even those ones were disappearing - it was as if I had dealt with the problem enough that my own body then managed to do what it should have done in the first place and "fight off" the infection - verracas are supposed to be self limiting and should eventually go away of their own accord (only I'd had mine for over 10 years).
I've had none now for over 10 years.
I suppose what I'm saying is that your softly softly apporach may well work - you're just helping your dd's body with a little bit of extra encouragement with the tea tree oil.
When I was about 12, my dad had "frozen" a verruca out for me with liquid nitrogen - maybe that's why they came back, and why this time, when my own body finished off the work, they haven't.