This is Monster, one of the kids' stuffed animals. We don't know anything about it, and I've never seen anything like it before. Their grandmother picked it up at a garage sale, so its origins are not known. There's a tag that says that it was made in China by a company called Toppy Craft.
The kids like Monster very much. And really, what's not to like about this weird yet cuddly character? I figure, at the very least, this guy will teach them not to be afraid of real monsters, or something like that.
Anyway, here are some drawings the kids made of Monster. The last drawing, lower right, is my work.