That looks like too much many destinations for too little time. I can't imagine spending only 1- 2 days, for instance, in D.C. unless you've already been here many times. If this is your first time to D.C., I'd allow at least 3 (and preferably 4) full days to visit.

I don't know how "scenic" Skyland Drive is going to be next week. It's been really cold here in Virginia this spring and they've had quite a few snowstorms in Shenandoah NP. The visitor center doesn't open until April 6th and then it's only open on the weekends until mid-May. Skyland Lodge is open for accommodations/dining and, according to the concessionaire's website, horseback riding will be available, weather permitting, beginning March 30th. Be prepared to dress warmly if you go to SNP.

Right in the middle of the Amish country of PA is the PA Train Museum in Strasburg. http://www.rrmuseumpa.org/visitors/calendar.shtml
Go to Philadelphia first to see Independence Hall and the Liberty Bell at least. Go to Strasburg and Lancaster. Dutch Wonderland won't be open until April 26. From there go to Washington DC. The cherry blossoms should be near peak by then.
Forget about trying to drive on the Skyline Drive.

You can do a lot in Philly in a short time as the city is compact. If the weather is nice, take the BIG bus tour-runs about 1 hour (tickets at the Bourse-near Independence Park.
http://www.bigbustours.com/eng/philadelphia/default.aspx

This takes you all around, and gives you a great overview of the city.
Independence Hall is an historical must, but the kids might be a little bored.

Depending on how you and your family feel about caged animals, the zoo is fun. The primate house is entertaining. Doable in two hours.
http://www.philadelphiazoo.org/

The Reading Terminal Market is the best place to eat lunch. Hundreds of stands-all types of food from all over.
http://www.readingterminalmarket.org/

From there you might want to walk up to Love Park at JFK and 15th then head to the Comcast center and check out the HD show on the lobby wall-really cool for middle school kids.
http://www.visitphilly.com/museums-attractions/philadelphia/comcast-center/?gclid=CLfN8dPKk7YCFSbNOgodHH0Arw

If the weather is really cold I also recommend the Franklin Institute-Titanic Exhibit-amazing and the rest of the museum is geared toward kids.
http://www2.fi.edu/

The Art Museum is really close by and although the kids won't find it as cool as the Franklin, there is a great armor room and Japanese house/garden.

Nearby is Jack's Firehouse-a great place to eat. It is actually an old firehouse. It is right across the street from the Eastern State Penitentiary.
http://www.jacksfirehouse.com/



If all else fails, there is always Dave and Busters (food isn't that great-but the kids will love the entertainment. All kinds of video games, skee ball, etc. Loud, busy, a bit tacky, but fun. This is also a bar-so it depends on how you feel about that.

One last thing most people do in Philly is have a cheese steak from Geno's or Pats. If you are vegetarians or vegans-not an option.

An outstanding place for Brunch-the National Mechanic Building in Old City
http://nationalmechanics.com/philadelphia-restaurant-menu-brunch

If the weather is nice-kind of doubtful, grab a map and take a walk around center city, or Stroll down South Street and make a stop at the Magic Garden-amazing and funky mosaic showplace.
http://www.philadelphiasmagicgardens.org/

Lancaster stops- Beware the tacky factor is high. Go to the Amish Experience on route 30, Kitchen Kettle Village, The Outhouse (wacky little store-fun for kids) maybe take a buggy ride. I agree with tomfuller's recommendation for Strasburg. Also Intercourse is a nice little town on route 340. Touristy, but interesting shops. Try some shoe fly pie.
Do not attempt to do anything here on Sunday-almost everything is closed.

Lots of ideas here.
http://www.padutchcountry.com/Presentation/ItineraryPreview?PreviewItineraryID=58506

You might want to consider adding Baltimore instead of Skyline Drive-The Inner Harbor is fun, the aquarium is beautiful and the American Visionary Art Museum is worth a visit. I think even your kids will like it.

DC is tough as there is so much to do, I think the Smithsonion Air and Space museum and the museum of American History would be best for the family. Lincoln Memorial is a must-skip going into the monument-the lines are long and the windows at the top are tiny. The best view is from the Old Post Office and there are plenty of places to eat there.
http://www.oldpostofficedc.com/
The tidal basin will be nice if the cherry blossoms are blooming.