Have you heard of this stuff called "Goo Gone" I remember in middle school some girl did a presentation with it… she put chewed gum in her hair and rubbed it around and this goo gone stuff took it all out, like it was nothing.
I'm not sure how friendly it is for pets... hopefully it says on the bottle. I've used it to get stains out of clothes a gazillion times! You can pick it up at the local hardware stores, or even in grocery stores. I've gotten it in the checkout lanes....
Good Luck!