Does anyone know...when you order your Wash. Monument tix in advance, do you get to pick a certain day/TIME?
That's the way it worked when we got tickets a couple years ago. If your time is mid-morning or beyond you have to be careful not to over plan so you get there on time. If you're not familiar w/ DC it's hard gauge how much time it takes to get places and how much time you'll want to actually see things. Yes, good photo ops from the top if the weather's good. Kinda tough on foggy/smoggy days.
Don't think you can get close to the Pentagon. You'll see a side of a big building from a distance - and the roads around it are BUSY and go every which way (it's a confusing area to drive if you don't know it!) There's no tour that I know of and they're not particularly welcoming there - very tight security.
Arlington National will take some time and by far the best way to see it is via the Tourmobile once you're there (you can take Metro to get there). Make sure you get off at all the stops! Don't recall much in the way of food available, do plan around meals.
Bureau of Engraving tour tickets are first come/first serve in peak season (early March+) which can mean getting there before 6am to make sure you get in. You will need to be flexible w/ your schedule that day since it's impossible to know in advance when your tour time will be.
The monuments are a march, there's just no other way to put it. IMO they're absolutely worth the time but be prepared to W A L K !!!
Do take time for the Museum of Art outdoor sculpture garden - next to Museum of Natural History. Good "bistro" food stand, not inexpensive tho.
Union Station is a great place to eat and spend some time (during the day). Better variety than Old Post Office Pavillion but maybe not as good a location for you, depending on where you've been.
You really do have limited time here and the museums can take a lot of it. There's not much on your "icing on the cake" list that I'd make time for this trip except the Capitol. I don't know anyone who's done the Supreme Court tour (assuming there is one) but it's a haul back to that building altho it's a neat building on the outside. It really looks like a Supreme Court IMHO

. Ford's Theater is meh to me, but YMMV. We like the Botanical Gardens between American Indian and Capitol - nice old conservatory building, interesting plants, nice change from everything else and quick.
Spy Museum is ok but not worth your time and $ if you're limited. About half the exhibit is about he Cold War and atom bomb development and use. That part's not real interesting to kids but the other exhibits are. In other words a mixed bag for your ages. Have not been to Holocaust Museum but will probably take my then 13yo over the holidays, think he's about old enough to put it in some perspective.
Check one of the DC Convention and Tourism calendars after the first of the year to see if anything interesting pops up for your time in town. As I recall there are a few good events that occur just before Cherry Blossom like the Smithsonian Kite Festival.
Lastly, IF you kids are really interested in Air and Space, take the time to go out to the Udvar-Hazy Annex of the Air and Space Museum out by Dulles. Easiest way to get there is by car (pay for parking, museum free). It's a BIG hanger building chock full of planes, etc. There's a Space Shuttle (surprising how large it is), a Concorde plane that fits cross-wise in the building, the Enola Gay, and lots of planes, old, new, big, small.
As you've probably guessed, the keys to visiting DC are prioritize your time, stay flexible, and wear comfortable shoes

. Oh - bring a jacket for every kind of weather in March!