M.R.
I go to Tysons all the time -- I live really close (nope, not in Sterling, not sure why Mamapedia listed that address for me!). It was just the local ol' mall when I first moved here, I've been around that long....Used to work in Alexandria, too, so I know the drive you'd make. Just time it so that you are not caught in traffic.
Best truly family-friendly option is not inside the mall but very close. You want to go to Silver Diner (go to the web site at www.silverdiner.com and click on "restaurants" for a link to the Tysons one with a map). It's just across the street from the mall, about one minute outside the mall doors.
Silver Diners can easily handle three very young kids. Large booths, extensive menu, kids' menu, usually the wait staff is great (I go to another one more frequently but generally the wait staffs are good at all locations). The diner is used to hosting a lot of families. We've been taking our daughter to SD since she was a baby and I often see families with lots of kids there, as well as kids' sports teams, etc.
Be aware that all Tysons restaurants including SD can get VERY full and busy, especially on weekends, so try to eat at a time that's a bit "off" the usual lunch or dinner hours if it's a Friday, Saturday or Sunday, or you might have to wait to get seated.
Inside the mall: You may hear that American Girl's restaurant is kid-friendly and it is but...there is often a wait to be seated, it's pricey (though the food is OK) and the menu is limited. I like it for a special meal out with my daughter but not for a shopping-day meal out, and not for really young kids who might not eat what they serve. FYI, I also go to Reston frequently from the Tysons area, and it's another 15-20 minutes beyond the mall so I myself wouldn't drive out there just to eat, if my destination were the mall.