I have kids similar ages. How about meeting up with a friend who has kids, or visiting an old friend with kids? I've done this solo and had success. Once we went to knoebels in central pa, another time I drove with the kids to see a friend in Cincy. The kids ran around, my friend and I kicked back, drank wine and ordered take out.

I'm currently "staycationibg " with kids while DH works. It's been fun... We've basically done more local things and ate more ice cream.

Westmoreland State Park in Virginia

Nemacolin, Rocking Horse Ranch (NY) Smuggler's Notch in VT all have kid's clubs for babies.

You could try Dutch Wonderland, 2 younger kids can ride the dinky kid rides and 1 year old goes in a stroller. The Strasburg Railway and little train play area, the DoubleTree indoor pool or similar, those smorgasbord restaurants are family friendly.
That said I did see a number of crying babies at Dutch Wonderland (DisneyWorld too!) whose parents were clearly pushing them too hard that day so that the older kids could have fun.
Also, a near-beach condo/1 BR unit at Rehoboth could work, 3-4 hour trips to the beach, lunch, naptime, Funland, pizza dinner and DVDs at the condo. I say condo because I'd want the W/D.
Any kind of water park, beach, lake or pool of much depth could get out of control pretty quickly when you have to watch 3 little kids like that. A spray park/sand box/playground, however, would be great.

When kids were younger we went to Grandma's house and took day trips like the ice cream factory, a pretty botanical garden/nursery, butterfly garden, zoo, minature horse farm, neighbor's pool. We had a nice vacation in Captiva, a vacation house near but not AT a VERY mellow beach like Sanibel or Captiva could work esp if you bring a family member or other mom friend with same age kids to help.
Community pool, no private pool.
Somewhere you can set up with a shade for the baby but not have to worry about the kids disappearing into a crowd or drowning.
State park cabin could work but I'd shun anything without a private bathroom and laundry facilities until the last kid is 3 or 4. Too much sticky/stinky/sandy accidents.

Oh possible a staycation site: national harbor.

OP, what kinds of things do you like to do? How well are you able to cope with the three kids around town eg, taking them shopping or to the museum? This might help you and DCUM gauge your ability to handle different places. If you're easily able to maneuver around the DC area without your husband then I see no reason why you wouldn't be able to cope on a sedate trip eg, camping, staying near a lake, Dutch Wonderland, etc.

Unless 1 or 2 more adults are coming with you, you're taking a trip, not going on vacation. I agree with others that you might be better off staying home and using the money to hire a sitter to have a staycation.