Not asking a lot are you ....
Firstly - catered chalets aren't that common in the states. There are a few companies which will do them, but your choice is pretty limited. Add in your other criteria and you may not have a choice of many (or any?) - I can't think of any off the top of my head and I'm fairly au-fait with the UK based ski travel business.
Are you thinking only of the US, or North America in general? Canada generally offers more value due to a better exchange rate, and a bit less immigration hassle (need to have thumbprints taken now for the US, etc).
Would you consider resort daycare, or a local nanny/babysitter arranged through the resort rather than by a tour-op?
How critical is the chalet aspect of it - do you want a chelt because it's self contained, or because you want the catering.
Give us a few more clues and I might be able to give you some ideas.
As a rule of thumb you might find if you go for a DIY option that the smaller resorts are better for young children - Smugglers Notch in Vermont, and Tremblant in Quebec both have good reputations for little ones (but they can both be cold, so pick your time carefully).
By the way - I do have some recent experience of this. My ds was skiing unaided in Canada this year at 2.7 , and both the family-friendly resorts we were staying at Big White/Silver Star were happy to do a combination of daycare and ski lessons with him at that age. No catered chalets there though, but some fabulous houses for rent which would be the size you'd need.
We stayed here which is a very child-friendly hotel (especially if you have train mad boys!)