I agree with the PP who pointed out that a teen who can be trusted to attend a concert by herself can be trusted to travel to the concert by herself. Others mentioned public transportation. If you live in or near a major city, there might be a shuttle available, especially if this is a big concert. If she or her friend has a license, would they be able to drive? (If you let her borrow the car, make sure she understands that she needs to take care of all tolls, parking, and gas herself. It's up to her to decide how to recoup costs from the others in the party.) An added benefit of doing this is that it would show her quite clearly that playing chauffeur comes at a cost to you.
I think that to address the overall situation, you should simply try to prevent it. When your daughter asks for permission to do XYZ and says that Joanna's parents have agreed to drive, ask her what the backup plan is (especially if you know that Joanna's parents are unreliable). Say something like, "Sure, honey, that sounds great. I'm not going to be available to drive that day, so what's Plan B if the Bartons have something come up and aren't able to take you?"
As for her getting mad that you won't step in and save the day, chances are that she knows that it isn't your fault. She's annoyed that someone else flaked out and the plans seemed to fall apart, then suddenly has a ray of hope when she remembers Mom. Then she gets disappointed again when it turns out that you can't do it. (It's sort of like when you get dumped and you aren't just mourning the loss of the relationship but also the future you hoped you would have with the person. While the future obviously was not guaranteed, it still burns.) Just remind her, gently, that when you told her that she could go, you had let her know that you wouldn't be available to drive. Offer to help her look into other options (cabs, shuttles, busses, trains, etc.) or ask her if one of her other friends has parents or an older sibling who can drive.
For this situation, that's exactly what I would do. When she comes home and is mad, remind her that you agreed to let her go to the concert when she had arranged for transportation. Say that you would not have agreed to drive her in the first place. Then immediately shift gears from saying no to offering her the help that you are willing to provide. (Get her and her friend to/from the local bus station, lend her the car, research taxi companies, etc.) If she complains or calls you mean, ignore her and repeat the offer of help, whatever it may be.