My initial reaction would be steamboat is a great spot for a family trip. But i just went and looked at my ski log and saw my last trip to Steamboat was back in 2003. So with a grain of salt, I do remember fantastic tree skiing, fun steep chutes, great restaurants in town and natural hotsprings an easy drive out of steamboat. Moving a big group between resorts sucks, especially with kids and beginners, so yeah steamboat should have everything you need. I've only ever flew into Denver and drove. I believe Steamboat's elevation is a lower compared to Summit County, if altitude sickness is a concern.
Looking back I see that 2003 trip was when i ripped an edge out of Salomon XScreams at copper.