Your poor daughter! :'( I hate scrinched toes.
If the new skate fitter does better, I suggest you also go to him for the adjustments as well, and drop the old shop altogether. In addition, shops with poor fitting skills frequently also sharpen badly (because it's likely the same individual who hasn't taken the time to learn to do things right), or take off too much metal while sharpening, which means you have to buy blades more often - though if she grows faster than her blades wear out, the latter problem may not be an issue.
It's not just a matter of initial fit and heat molding. He can also stretch the leather right next to the toes. If the old fitter didn't do that, after each heat mold, then that fitter wasn't competent, or didn't have the proper equipment. The new fitter can stretch the old boots a little too.
I suggest that until the new boots arrive, you remove the insoles from the old boots to make extra room. (You may have to pull fairly hard, as some insoles are held in with mild glue.) If there is anything rough or sticking out on the bottom of the skates that might hurt her feet, you may have to trace the shape of the insoles on something very thin - e.g., thin cardboard - and cut it out to create very thin new insoles, to let her feet sit on a smooth surface. If the heels are too wide with the insole removed, and are moving around (potentially creating blisters) put an appropriate thickness of tape underneath the heel of the new insoles.