As a denizen of Old Town, I would say the most kid friendly is Chadwicks. Pita House and Majestic are not really kid friendly -- both in food or size of place. Austin Grille and Bertucci's on King Street (about 4 blocks from water) are very kid friendly too. Hard Times is also good but a bit further away on King Street. Of course it depends what you mean by kid friendly -- food wise? Accepting of children? kid menu?
You didn't specify which Sunday...so maybe this is too late. Two places that are particularly kid friendly are King Street Blues and Hard Times Chili. There are also BGR and one of the first 5 Guys in Old Town too. And, if the kids like fish, Eamonn's can be fun just because it's so differnet.
Hmm, the links don't seem to be working correctly. Here are addresses, all are Googleable:
King Street Blues, King & St. Aseph
Hard Times, King & West Street
BGR, King & Washington St.
5 Guys, King and Colubus
Eamonn's, King and Columbus
King Street Blues
112 N Saint Asaph St, Alexandria, VA 22314
Hard Times Cafe Alexandria
1404 King St, Alexandria, VA 22314
728 King St, Alexandria, VA 22314
The Burger Joint
106 N Washington St, Alexandria, VA 22314