You're welcome!
For lessons for the kids, Alta would be great based on my daughter's experience. Also that of the kids of my friends in the past 15 years. Solitude is family-friendly for travelers so I expect their kid lessons are also good. Brighton caters more to local families. School buses pull up every afternoon midweek.
I have no doubt that Park City and Deer Valley are also good for families with kids who are learning fast.
I was an intermediate who hadn't skied much as a working adult when I started my daughter in ski school at Massanutten at age 4. Between Mnut ski school and Alta ski school during spring break trips when she was a tween, she was an advanced skier by age 11 and clearly better than I was. Took several years of lessons at Massanutten, Alta, and other destination resorts out west for me to get to her level. My husband is a non-skier with no interest in traveling on a ski trip, so I ski with friends. Of course, helps to be retired.