And, again, I say for 4 hours with a ten year old girl on the first day, Deer Valley. You won't have crowds, the snow should be fine, you won't have to worry about borders on her first day navigating down the mountain, and it's Deer Valley.
Take her up on Wasatch Express and look to your left as you get to the top and show her the expanse of the Jordanelle resevoir. Then take her down Sunset to Ontario, all the way to the bottom.
Sure, you'll have opportunities to ski it on subsequent days, but with just you and her, it'll be a great and stress-free choice to get some dad and daughter time. Have fun whatever you decide and be careful.