Unfortunately, i think that the closest drive you will be able to get is about 2 hours. i know of two resorts that i have gone skiing and snowboarding at.
First is wintergreen resort. it has a lot to offer however, it is too often over-crowded. i have skied and snowboarded at this resort and it would be better for people who already know how to ski/snowboard. it is a nice place other than the possibility of 1 or 2 hour ski lift lines. Meaning you will probably only get 5 or 6 runs a day.(which may vary depending on your patience and tolerance to the cold.
Another place i would suggest would be Massanutten. it is near James Madison University in Dayton, Virginia. It is much smaller but has a great kids ski/snowboard program and two great beginner slopes. It also has some very advanced slopes if you ever decide to go without your children. i have also skied/snowboarded at this resort and i would suggest it over wintergreen becuase there is never a wait and it is extremely family oriented. i have gotten into 25 runs a day at this resort. And if you lose the interest to ski one day they have a great snow-tubing area which is also very fun for all ages.
I personally would suggest massanutten because you get much more skiing time and it is a safer, more family oriented environment.
Hope i could help!!
I personally would suggest massanutten for your trip