Okey dokey, so a bratty mare, eh? Well I have a method for you. I hope it works! You obviously could tweak it if you need to.
Everyday your friend comes down to ride her, make her ride in the ring by herself. Don't let any other horse in. This should temporarily solve her issue of being left behind. If she is alone, she has nobody to be left behind. If she still bucks, then you have a whole other issue.Have your friend ride her for 1 week with no other horse.
The first day, bring her in the ring with other horses, but hand walk/trot her. Trot her behind other horses and make sure you do the things she normally gets bad at. Carry treats. Every 2 minutes or so that she is good, give her one and reward her. If she is bad, halt her and back her up 2 steps.
The next days have your friend, or someone who's not nervous to ride her, get on her and do these things she gets bugged at. Give her treats while you are riding her if she is good (if possible) and do many figures (figure eight, circles, etc) to keep her attention on the rider. If she bucks, halt her and bac k her up 2 steps
Continue doing this until she stops. Good luck!