I'm a local.

I think you'll really enjoy your hotel location and if it were me, I'd just stroll the 2-3 blocks south toward the White House and Layfayette Square and see the fireworks from that vantage. The Mall will be very crowded due to people getting spots early, so it probably isn't the best day to do the museums, but the fireworks are visible from all over -- and there are no tall buildings in DC so you should be able to get a good look from just about anywhere near where you're staying. Best of all, you have an easy stroll back to the hotel -- no cabs or Metro needed.
There are museums away from the Mall area that are fun for kids -- they are not part of the Smithsonian, so there's usually an entrance fee. Spy Museum, Wax Museum, Newseum, etc., are away from the Mall madness and a reasonable walk. The historic sites, like Archives and the Capitol, are probably best for a future visit than on a holiday weekend!
I like the Gravelly Point suggestion, but honestly, you're staying in such a convenient downtown spot I would be loath to leave it. Enjoy the amenities of that location! What a fun birthday surprise.