start with hot dogs and mac and cheese. add pasta in any form. If mom and pop want a steak make it for them, but feed the kids what they will eat and enjoy eating. Use booths with very high backs to prevent adult complaints and if possible no tables. Children as a whole are messy, teach your people to clean under around and over. Forget the mood music, the children will provide that hopefully with lots of giggles and very little whining and crying. learn to create faces or something on everything from pancakes to toasted cheese sandwiches. Children love dips. so provide them. put paper towels and cleaner where parents can reach and children cannot for that spilled glass of what ever.
Advertise as casual dress. That will tell the world you are not looking for that finiky idiot that hates kids. Keep the kids happy and carefree and the parents will return over and over.