Saying "OK" on the second just-in-case ask ('cause that's what it was) is most definitely not saying "No."
I agree with his mom (who shouldn't have called you) that she needs to be clear, explicit, and probably apologetic.
"Jay, I'm sorry I wasn't clearer before. I am not going to go to the prom with you or anyone else. I'm busy that night. Good luck finding another date."
Yeah, reading that interaction made me think she'd opened the door to the possibility that she'd be going with him. I think she should approach Jay in person and apologize for the misunderstanding the other day, but as she told him when he asked originally, she is going to be busy that night.
I think that was pretty manipulative of Jay, to say "let me know if you change your mind," and then act as though her "Okay?" was a yes.
I agree you were out of line ot ask that mother what is it she thinks should happen.
Your daughter should say to Jay, "Listen, I told you the first time you asked that I have definite plans for the prom and am not going. Then you said I should let you know if I changed my mind. I didn't let you know, because I didn't change my mind. I have plans, and a commitment to my babysitting family. I'm not going to prom. And I told you that the first time you asked me.
"In fact, Jay, you cannot blame me for the fact that you bought tickets and a tux and everything else. I told you I wasn't going. That's on you."
"Oh, and you know what else, Jay? Tell your mother not to call my mother. This is between us, and I'm not going to prom with you. I told you that the first time you asked me. Excuse me, I have to get to class."
I agree w/ Nemesis, to a large degree, and w/ miranova.
I'd want my girl, however, to feel that she could say, "Jay, I told you already, I'm not going to prom. I have a babysitting commitment. I don't understand how you could think that means I'm going to change my mind, and I don't understand why in the world you'd buy tickets with ME in mind. I'm not going to prom. And now I'm not ever going anywhere with you."