Welcome to RTA!
The BRP should be open in April, but anything is possible.
It's about 400 miles from Asheville to Waynesboro, and another 105 miles from Waynesboro to Front Royal on the Skyline Drive. It can be driven in 3 days. To give you more time on the BRP/Skyline, I'd spend the 3rd night in Front Royal instead of Frederick, it's about 5.5 hours from Front Royal to NYC via I-81 and I-78.
Where to spend the 2 nights? Possibly Galax and Lynchburg?