Hey, I learned something new today! It's always a good day when you learn something new. I didn't know a noavel was a bitless bridle.
Sounds like your mare is left sided. In other words, it's harder for her to turn to the right than the left. Horses are right or left sided, just like people. If she'll longe to the left but not the right, that may be the problem.
Is she alone at your place or does she have another horse or a companion animal? If she's alone, that could be causing part of her issues. Horses are herd animals and can get panicky and ill mannered if they're alone.
Plus, who besides you worked with her when she was at her previous owner's? If there was someone more experienced helping you, the horse may have acknowledged that person as the leader, and not you.
Is your friend more experienced than you? If she is and the horse was responding better to her, then maybe you're confusing the animal with unclear signals.
You said the mare is green. If you're also green that's probably where a lot of your problems lie. Neither of you knows how to communicate properly with the other.
Rearing is a no-no in my book. I have a gelding who used to try that with me. A few Come to Jesus meetings, and he learned that behaviour was completely unacceptable.
You may just be in over your head with this mare, and there's nothing wrong with that as long as you realize it and get some help before either of you get hurt.