There's a lot of that out there if you pay attention. Though it wasn't a cartoon (not exactly) Pee Wee's Playhouse was rife with inside jokes for parents watching along. Even Arthur on PBS Kids has them sometimes, but they're more innocent than bawdy.
You know what's rarer? Children's jokes in adult movies. Can't even think of any.
Just out of curiosity, how many adult movies have you been watching to check for kids jokes? Did you check equally across a wide variety of the various subgenres of porn?
That's true, they could be out there since the only two porn movies I've ever actually watched were called Shaving Ryan's Privates, which was funny WWII themed straight porn in which an Iowa farm boy with a lot of body hair meets a nubile French beautician right after D-Day, and Sack Lunch, which was involved gay men doing something to each other that looked painful to me.
I guess I have caught bits and pieces (ahem) of adult fare here and there though. As for your question, no, no children's jokes in them at all.
Maybe we could create the genre of juvenile humor in adult.... Nope, forget that thought, that sounds like a good way to get arrested.