At that moment all I remembered of riding double was never a problem even on random horses that were barely ridden.
you lucked out. What I remember about riding double on a horse that had 6 months riding was a bucking horse, bruised riders and a walk home.
To be fair to a green horse, you need to do everything carefully, and with preparation. If he had never been ridden double, you should have sat where the second rider would sit and tried riding like that, flapped your legs around in that position to make sure he was comfortable with legs near his flanks, and then saddled him up and bridled him, so you would have had the best chance of control, which would have ended in a positive experience for the girl, you, and the horse. Now he has had a bad experience, you will have regressed, and will have a horse and a girl who will have to be worked through their issues.
Back to the point, if a horse starts bucking, you need to do a one rein stop, disengaging their hindquarters, then you have to get them through it. If it was fear based(like this one), you should have taken the girl off, done some desensitizing, perhaps led the girl around(to finish on a good note for her), then continued on the lesson of carrying someone double, by perhaps sitting in that position yourself, desensitizing around the flanks, etc. If it was disrespect, you should put them to work in no uncertain terms.