Book in this order
1) Dates that are not Christmas week unless you like crowds. 2) Lodging with a kitchen and a place to dry gloves. 3) Ski school — this is the one that sells out, not the lift ticket. 4) Flights. 5) Gear plan (rent on the mountain for first-timers; own helmets). 6) Pass vs. day tickets. Reverse that order and you will be waitlisted for lessons with a crying 5-year-old in the rental shop.
Pick the mountain for the smallest skier
The trip is only as good as the least-happy child. A 'legendary' mountain that terrifies a first-timer is a bad mountain this year. Brighton, Okemo, Smugglers', Keystone Kidtopia, Solitude Moonbeam, Deer Valley — those are first-trip mountains. Alta is a later trip. Vail is a later-and-richer trip.
The day-one template
Sleep. Water. A short rental fit. A two-hour lesson or a magic carpet, not a summit photo. Lunch early. Quit before anyone cries. Dinner at 5. You will feel like you under-skied. You will have a second day.
Salt Lake vs. Colorado vs. Vermont
Flying with little kids: Salt Lake, because the transfer is 35 minutes and you can still grocery-shop. Driving from the Northeast: Okemo or Smugglers'. Already on Epic and coming from the Midwest: Keystone, then Breck for a town dinner. Already on Ikon: Steamboat if you can reach it, Winter Park if you want Denver without I-70.
What success looks like
They want to go back. That's the only KPI. Not vertical feet, not a tram selfie, not whether you got your money's worth on a 10:30am chair. If they want to go back, you can take them to the interesting mountains later.