they aren't your "family" anymore......and as you are now EX'd that means you start EX'ing yourself from his family. sorry, but it's the way it goes. and since you are already so conflicted about attending and what may or may not transpire, who may or may not be there etc, that's already more baggage than the EVENT calls for.
you drop off the blanket and a card on another day, and express your birthday wishes and appreciation for the invite. and then you go on your way.
see the day isn't about you.......or your ex. it's about a boy who is turning 13 and an adult. and presents and cake. but you and the ex have a drama-rama which really has no place at such a function. etiquette and all that.