I've done the VT road trip thing on at least thirty occasions with and without kids.
Do you want to hit a number of ski areas or just a couple?
There are a number of towns that you can stay in that have chain hotels, mom & pop motels, B & B's, & Inn's. Most of these towns you can ski 2-3 areas that are between 5 - 60 mins. away.
Bennington or Manchester - Mt. Snow, Haystack, Stratton, & Bromley, Magic
Rutland - K-mart, Pico, & Okemo
Waterbury (I89 & Rt100) - Stowe, Mad River, & Sugarbush. There a is Ramada (? chain hotel) about 1/4 of a mile off the Interstate that is about 1/2 way between Stowe & MRG.
Some trips we'd go further north to Jay & Smuggs. But we found it harder to get last minute reservations at Jay.
If you want to stay slopeside; Okemo is very family friendly and has a ton of slopeside accomodations. Killington & Sugarbush are both huge ski areas and they also have a lot of slopeside accomodations. I think Stowe is a true New England ski town and the ski area has a lot of really long trials. Plus Ben & Jerry's Ice Cream factory is on the way to Stowe.
Try Ski Vermont