The short version is that while you had an invite to this party, the mother of the birthday child got greedy and it blew up in her face. Now she's going all drama on K and K is going all drama on you and if it were ME, I'd say, "I'm not in middle school, you should tell J that she messed up and she should put on her big girl panties and deal with it." Then I would feel sorry for J's kid, but not attend if there was going to be this much drama. My kid doesn't need it. I might even tell K that she shouldn't go, either. I bet she's used to being bullied by J and needs to stand up for herself. I wouldn't go to support K because I don't need to get a babysitter for middle school drama.
Were it MY husband, I'd darned well tell him to pay the vendor directly. Especially with an unstable ex. So HE was going to step up and pay til he realized she lied, so the whole thing is J's fault for not taking the generosity of her friend in the first place.
When someone says their ex is crazy but they like drama, always be suspicious of her version.
I feel bad for her kid.
ETA: If I were K, I'd also back far away from this drama in my workplace. It could come back to bite her if it goes really badly. Sounds like J doesn't fall far from the tree, either.