Kid Friendly in Rye/White Plains area
I know that PF Chang's is a chain, but my children always love it. Plenty to entertain them with, especially these sticky wax sticks. I was going to suggest City Limits, again extensive kids menu, but lots of interesting food for parents, but they are under renovations. We take our children out for dim sum too at Central Seafood on Central Avenue. The children like the soup and dumplings, while the adults enjoy the more interesting parts of the menu. It's more casual that Aberdeen, and the children like to look at the fish in the aquarium. Just don't tell them that they are there to be served as lunch!
If you (and your parents) like tacos, in Port Chester Bar Taco is fun. Again, you can sit outside and watch the boats while you wait for the food. The child will love the churros dipped in chocolate for dessert.
(wrote above before I saw the sentence -- loves pancakes) You can introduce her to pancakes from around the world. Moo Shoo Pork at Central Seafood is served on Chinese pancakes, and the tortillas at Bar Taco are just Mexican pancakes.
For traditional breakfast, your best bet may be a diner, however, there is Eileen's Country Kitchen in Yonkers. They do a wonderful breakfast.
I think you might have to settle for a diner if you want pancakes. Aside from that, most places in White Plains attract business people dining at lunch time. Probably won't be crowded, but not necessarily kid-friendly. In Rye, there's always Kelly's Sea Level or Rye Roadhouse. I've seen kids in both places when I've been during the day.