I would avoid cutting across the DC Baltimore corridor and the Bay Bridge. First leg go to Harrisburg Pa I76 a pain or I80 to Clearfield and US322 a little longer but easy driving. Then head to Lancaster Pa I283 then US30 to Gap Pa then S on US41 then S on DE7, you will be still in PA when you turn on to it. Stay on DE7 it turns into DE1, then at Dover DE US113 S to Berlin MD then follow the signs to Assateague. At Berlin there as a Food Lion for last minute items.
Lancaster Pa would be a good stopover, Old Millstream Campground, or if you are looking for a Walmart the one at Parksburg is good for a nights sleep you can take PA10 to US41 from there
We make the trip from central Pa to Assateague a couple times a year.
1999 Dodge 2500 Diesel QuadCab
2005 Desert Fox 28KS