The kids generally prefer hotels because they have pools.

We've found plenty of professionally run "resorts" where the space is like a small apartment, with a full kitchen and multiple bedrooms. These tend to be right in ski areas where we could walk to the lift if we were staying during the ski season. We did stay in one that was AirBNB-like because it was privately owned but the ski area handled the reservation and any issues that came up while we were there.