A-Basin should easily meet your desire for a single base area & plenty of terrain variety. Cost is good too ? (I had a Heavenly pass that worked.) Was there with my 10 yr old for this trip http://forums.epicski.com/showthread.php?t=70030
in May. There is above treeline, groomed runs, some gullies, kid sized tree runs etc. avail. from an uncomplicated lift system.
Single base lodge with all the terrain on the front side feeding to it if a wrong turn/trail is taken. A mid-mountain lodge & the lifts from there to the top with most runs leading back to the mid mountain lodge/lifts is nice with a kid. Or ski on down to the base area for a long run top to bottom. Montezuma bowl is one little traverse up & 1 lift out with lots of choices for dad to ski while she's skiing to the bottom of Montezuma.
She'd be hard pressed to find her way over to the Pali Lift, ending up in expert terrain. Didn't experience their ski school. For peace of mind, a set of FRS radios would be nice. Probably not needed. At 10yrs old, we have started going over trail maps, base area, lifts, etc. Where is ski patrol located on the mountain & base. If mom doesn't show up at the bottom, which run were we on & where'd you last see me at. What do you do, where do you go.
If you're staying in a town off I-70, you have so many choices if you want to try a day at another resort. All very close. You two should have a blast !