i don't count toddlers or babies as kids. They're a whole separate group to me. There's a reason there's a Disney Channel and a Disney Junior, that there's a Nickelodeon and a Nick Jr.
I count the Middle as a family show. I count The Neighbors as a family show. These two are shows whose target is the entire family, not just kids and not just adults. They're marketed that way. My Little Pony is marketed at little girls.
You just described Rugrats, Dexter's Laboratory, Powerpuff Girls, Dragonball, Catdog, and just about every cartoon worth it's salt.