Domo Animate has a studio where you can create your own animations. You need to register, but that is the usual quick process. The editor is simple - a matter of dragging characters, backgrounds, effects, music and objects to your working screen. You can make changes like flipping, moving forward and back, altering the handle on the speech bubble etc, as well as add emotions and movements to characters. You can preview, make changes, then save and get an embed code, or share with your friends.
There's also a tutorial you can watch to get you started, but I don't think your kids will need it.
This is a great online place to engage kids in creating their own comic-type stories, with just enough writing to drive the story forward, but not so much as with a narrative. Longer texts are daunting for some kids. You can add lots of scenes (I got tired of testing this function at scene 18), and there's a long list of music to choose from. I like the different styles of characters you can have, too - as well as classic cartoon figures, there are stick figures, Domo figures, monsters etc. One more great feature: you can take a screen shot like the one above, and save it as a jpg on your own computer. The animation part of it is actually minimal, but I don't think that hurts. Kids can think of it as a kind of hybrid comic/slideshow.
I hope you'll give DomoAnimate a try with your children. Here's a sample one I made below.
DomoNation.com: Bigfoot by bookchook
Like it? Create your own at DomoNation.com. It's free and fun!