From what I'm aware of, everyone that has had the CML return have returned to the same dosage. Perhaps he is super keen to get your daughter back to negative, but he's not the one experiencing side effects. I think one or two of our FB members have taken the opportunity to switch TKIs at this point, but that is more about side effects and trying a different strategy.
There was no suggestion from my doc about doubling the dose if my CML returned and my doc is conservative, hence why I am still doing two monthly blood tests at 3 years. My doc refers to the Australian Stop trials. I would push back if my doc tried to double the return dose. I am also aware of someone that was on 600mg Gleevec trial for stopping and his CML returned in around 3 months. More dosage isn't necessarily better for somethings.
Also be aware there are blips for some people stopping, so keep an eye on test results, loss of MMR is the return point, not a blip. Monthly monitoring is good for the first six months, oddly my doc decided two monthly from the start, go figure.