Unfortunately, you won't be able to attend the Easter Egg roll. Tickets were distributed through a lottery which closed at the end of February.
We locals generally suggest using Metro to get into the city if you are staying outside of D.C. because traffic is bad and parking is both difficult and expensive. If you drive into D.C. for a day of sightseeing, you will need to find a parking garage because on-street parking is difficult to find and is limited to just a few hours, i.e. you can't park there all day. With a family of 5 (each of whom will need a farecard to ride Metro), it may be more cost-effective to drive into the city and park. I have heard that the parking garage at Union Station is a great deal because you can park there for 12 hours for $17 or longer for $19.
You may find it difficult to find accomodations for a family of 5 during Easter week for $125, especially since you will likely have to pay for parking too.

I've been to DC numerous times on business over the years, but I took my two boys (then 12 and 9) to DC for fun a few years ago. My husband was working on a long term project in the Baltimore area and had a corporate apartment. We came out to stay with him for a month--it was great. DH dropped us off at the train station and we took the metro from Baltimore into DC 6 or 7 times (we did other multiple day side trips all along the coast as well). The metro is probably the cleanest, easiest to use public transportation I've seen anywhere in the world. You'll be fine with a collapsible stroller--I'd consider one for the 5 year old too in case he gets tired. My children loved the National Zoo, the Air and Space Museum, the American History Museum (they saw C3PO from Star Wars, etc., lol), the changing of the guard at the tomb of the unknown soldier at Arlington, the Spy Museum, and the Museum of Natural History. If you want to avoid all the walking (we did the walking--I'm pretty fit but I was still tired) I believe there are bus tours that start and stop at all the national monuments. Make sure you get a metro map--you can jump on and off to get closer to different sites as well. I'm not sure how younger children would hold up for this, but the Holocaust museum was a life changing experience for our family (my husband's roots are in eastern europe). You can easily spend an entire day there, but it's intense. If you decide to go, you'll need to book reservations in advance online--although the Smithsonian museums are free, they'll give you a set time that you can show up to visit the Holocaust museum. You'll have to call your Congressman in advance to set up a tour if you want to visit the White House.

April shouldn't be bad as far as humidity--we were there in July and it was miserable. I made sure we wore comfy walking shoes, cool clothing, and carried bottled water, snacks, and sunblock in a backpack. We packed lunch and did a couple of picnics at the National Mall--the kids could run around and play. If you have bottled water with you, be prepared to drink part of it in front of security guards before you enter the Holocaust museum--the security is understandably very tight. If you're on a budget, I'd avoid the museum restaurants at all cost--they're pretty expensive. There are tons of street vendors selling hotdogs and drinks, etc., in the area.

One more comment--if you're planning on the zoo (and I'd recommend it), it's no where near the "mall" and most of the museums (the same with Arlington). Even if you drive in, you may want to leave your car and hop on the metro if you're planning on doing other stops that day.

I would think all the kids would enjoy the Air and Space museum. If they are not used to subways, the metro would probably be very interesting for them even though adults don't look at public transit as a source of entertainment.

The Clock Tower of the Old Post Office Pavilion has free tours, great views. There is a food court, entertainment on weekdays

Vttraveler--we're from Nebraska, where public transportation is a real novelty. My children LOVE riding the subway, trains etc. whenever we have a chance. I make them responsible for helping to navigate--not only is it fun for them, but hopefully they'll feel comfortable going from point A to B anywhere in the world when they're older and venture off on their own. It's a great learning experience.

huskermom--my kids both grew up in rural Vt and riding on subways and trains was always fun for them. I agree they learned a lot by buying tickets, navigating, etc. in New york, Boston, Montreal, Paris, Munich. My younger son was quite proud of himself when he was able to figure out the DC metro during a trip in 8th grade when most of his friends were totally overwhelmed.

I also tried to make them read street maps and plot our walking routes.

Thanks all for your help and advice! I just checked the whitehouse.gov and saw the lottery for easter egg roll is closed. I didn't realize they put the lottery online. So I guess we will miss it. However, we are waiting to see if we will get tickets to tour the White House (at least that I did apply for). Am leaning towards Omni Shoreham in Dupont Circle as they have a special promo.

FYI the Omni Shoreham is not in Dupont Circle, but it is a nice hotel and very close to the Woodley Park Metro station.

Which is the closest metro station to the zoo. It's not THE most central hotel to the mall area but the Omni Shoreham is a good place.

The Omni Shoreham should be nice. There are plenty of restaurants nearby and it is within walking distance to the zoo and Metro stations. If you stay there you can count on using Metro to get around. Strollers are fine in DC and on the subway, but bring the smallest model you have and try not to be on the subway from 7am-9am or 4pm-6pm when it's busiest.

Along with the zoo and the Museum of Natural History, the Air and Space museum is popular with kids. The fountain near the National Gallery of Art will be nice for the kids if it's turned on for the spring/summer yet. There's also a statue of Einstein along Constitution somewhere around 21st Street that kids like to climb on.

Definitely wear comfortable shoes and be prepared for a lot of walking. There is a food court in the Ronald Reagan Building if you want to skip the museum food courts due to price. That's also close to the postal museum with a view that someone else mentioned. If you end up near Chinatown or the Verizon Center there are a lot of restaurants in that area. Or you can always bring your own sandwiches and picnic on the mall somewhere. Have fun!