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Since it isn't making progress with conservative measures, your doctor is probably going to have to incise and drain it. It's always best with children to try everything else first because it is an uncomfortable procedure even with lidocaine. I hope she feels better soon.
I'm saying that it is one stubborn boil! What you don't want is for the pus to harden so that a large incision has to be made to remove a "chunk" of tissue and leave a big old scar on a cute little girl's backside. Ideally, the warm compresses/baths would soften up the outer layer and it would come to a head and break open on its own spewing its contents out.
You mentioned that the area got "dry" again between baths. The procedure generally recommended is to pat the area dry after the hot compresses or baths, apply an antibacterial ointment (over-the-counter, your favorite brand), and a bandaid or non-stick gauze dressing if it is large. That way the area does not become dry, and it encourages the boil to come to a head. You will go through a lot of ointment and bandaids doing compresses several times a day, but it will keep the area soft and encourage draining.
If this method doesn't work in a week, I would want to go back to the doctor to review the situation and discuss the I & D procedure.