I am going to disagree I think the OP has a case here. The Captain screwed the pooch, he should have come out of the cockpit and talked to the OP and assessed the situation. Instead, he passed the buck and bounced the OP. So they all screwed up.

The FA or whom ever started the incident by hollering at the PAX. They would probably get about the same response from me if I was hollered at. Of course the OP did not help the situation by telling the FA they had a bad attitude. Something more along the lines of - I do not appreciate being hollered at, if you need me to do something like gate check my bag please ask respectfully. That said my bag will fit under my seat. Thank you. The second comment was not needed.

That said had the pilot come out and dealt with the situation with perhaps a warning to the OP and FA that everyone needed to check their attitude a bit then everyone could have flown.

Given the above I would send the bill for the other tickets to JetBlue for IDB, as well as sending a letter to DOT. In the end if not paid it would be off to small claims court.