D.B.
What are the ages of your kids, how long do you have, and how much do you want to spend? We spent many vacations at a resort on Lake Champlain called the Basin Harbor Club. It's a family owned resort with tons of activities - lake, water sports, pool, kids' program, hikes, maritime museum, fishing, lake cruises, canoe rentals, etc. There's a main lodge and tons of cottages for more privacy, but all the meals are provided. It's not cheap but it's hassle-free. Kids can go into a program and the adults can relax or play golf at the excellent golf course on site. Lake Champlain was key in the Revolutionary War so there are historical sites if your kids are old enough to enjoy that.
The mountains are legendary, of course, and many of the ski resorts make money in the summer by having rides down the mountain and of course the scenic view from the chair lifts. The ski condos are available for rent year-round if you want a place where you can cook meals and just go out when you feel like it. Places like Queechee Gorge are fun to stop at, and there's stuff to do in Shelburne. Some of the towns are quaint with shops if that interests you.
You can go into maple sugaring places and cheese places pretty much anywhere in the state, although the activity changes based on the season.
Vermont's a LONG state so there is plenty to do, but you have to decide on how long you want to drive. It's not full of interstate highways - there are a lot of 2 lane roads that wind through mountains so you have to be patient.