Yeah, I'm with ML on this one. DC is beautiful in the spring. Now, of course this year April decided it was still winter, and we got snow. But that's unusual. BTW, Fairfax County (huge DC area school district) has spring break Mar 30 - Apr 3. DCPS is the week of Apr. 13.
If the choice is April or July, hands down April. June isn't as bad. But keep in mind, DC is crowded with tourists in June and July, as well as grumpy residents looking forward to their August vacations.
And for goodness sake, stand on the right when you're on a Metro escalator.
I think DC is one of the best places to vacation, especially with kids. There's so much to do, and most of it is free.