I'm late to this so you may have already come to a decision. I live in Salt Lake and we have skied at almost all the local resorts over the past 14 years. DH is a snowboarder so we don't go to Deer Valley or Alta, however. As far as ski school goes, we loved Brighton, but DS had a really great experience at the Canyons too. Brighton is always referred to around here as the "locals" resort. It doesn't have much at all in the way of amenities, honestly, and it's pretty isolated from anything that does. It would not be my first pick if I were traveling here from across the country for my first visit.
If you were traveling without kids and were really serious skiers then I would say go to Snowbird. The snow is generally the most reliably good there and there is a decent resort feel. There are several excellent restaurants and the skiing is a lot of fun. Again, though, it's pretty isolated. We never used the ski school at Snowbird so I can't comment on it.
Personally, for a vacation with kids, I'd choose to stay in Park City and ski at the Canyons. If the cost of staying at the Canyons is really prohibitive then I'd definitely look into a VRBO nearby. Park City just has SO many more amenities and conveniences. I really wouldn't want to have to travel 30-40 minutes daily to get to the resort with 3 kids.
Daniele
mama to
dd1 watching over her brothers and sister from Heaven
ds1 13 years old
dd2 10 years old
ds2 6 years old
Placenta Increta/c-hyst survivor