I lived in the DC area for almost 17 yrs. When we first moved there DH was in the USAF and we lived in Laurel, MD and then on base. We also lived in Columbia, MD. When he left the service we moved to VA and lived there in Fairfax for many years. I think it's better to live in VA because it's closer to the Pentagon and the commute will be less than if you live in MD, and yes, you should worry about the commutes. (When I moved away it took me over an hour to go 12 miles to work.) Also, will you all have two cars? If not, you want to be close to public transportation (not always a possibility in the US) so make sure you have bus and/or metro (that's the subway, or as they call the Tube in London) access. Another possiblity is where the commuter train runs, but you will be a lot further out from the metro area.
I would not live in DC under any circumstances as the schools are terrible. There are good and bad areas, but it's not as bad as the reputation ..just don't go into SE under any circumstances and NE isn't good either. The western part is the best. SW isn't good to live at, but congress and lots of govt. bldgs. are located there so it's pretty safe in daylight. There are some nice neithborhoods, but Georgetown doesn't have metro access and parking/traffic is awful. Also, DC doesn't have proper amenities such as shopping and you will have to go to VA or MD for major shopping anyway. The best schools are either in Montgomery County, MD or Fairfax, Co., VA. The suburbs are also more family-friendly with lots of parks and stuff.
Re: supermarkets, I keep hearing about how the supermarkets are horrible in the US, but I think outside of Waitrose, they are pretty bad in the UK, and there's so many things you can't get in the UK and you can get almost anything in the US. Whole Foods is wonderful, Wegamans's is good, Trader Jo's too. The major markets are Giant or Safeway, and the discount ones (Food Lion, Food 4 Less, etc. ) are good for paper goods/canned items, but that is about it. Sutton Place Gourmet is also wonderful. Get a membership at Costco and you can buy items in bulk which are a lot cheaper, and don't worry about space as you'll have a large, US refrigerator. Americans shop less often and buy a larger number of items on each visit.
You will probably think the bread tastes sweet, or at least that's what I've heard from others, but try Whole Foods and Trader Jo's first. If you don't like them, well then you probably won't like the others, but that's a good start.
We loved living in the DC area, but got tired of the long commutes and work hours. If you didn't put in a min. 10 hr. day, you were a slacker and might be laid off...Americans work too many hours, but that's just the way it is, but the US military is not bad about this on a day-to-day basis as long as you're not deployed so it will be fine fo you DH too.
Be sure to visit the Shenandoah Mountains, eat some crabs in MD and go to the beach a lot while you're in the US. There's so much to do in that area, and a lot of it is free. Also, Americans don't hate kids, and they are welcome in just about any restaurant. You don't have to eat crap to eat with your kids. Enjoy your time there.