Well, I am into Parelli, as you know, so I'll give you some ideas to work with that ARE Parelli.
If a horse is gate sour, usually that means she is unconfident. She doesn't feel safe and in her mind, safety is with her herd, so she will try to get back to them. So in order to fix this it first starts with your ground perperation. Do not get on until she is mentally, emotionally and physically relaxed. Just follow the program....it won't lead you wrong. When you ride take notice of WHEN she gets gate sour. Is it when you ask her in a certain gait? Does she start the behavior as soon as you get on? Is she tense? Etc. When you feel that FIRST sign of gate sourness bend her softly with one rein and ask her to stop and relax. Don't release until she gives, just like in Level 1. You could also stop and back her up a couple steps, but softly. If she is indeed unconfident getting after her will NOT fix anything. Have you tried the mirroring exercise? I saw Linda Parelli instruct a student with a gate sour horse at a tour stop and she had the rider walk the horse around on a loose rein and mirror his horse...when she looked left, he looked left....when she turned, he turned.....when she went to the gate and stopped he stopped with her. He waited until she relaxed and then asked her to go again, but he did NOT tell her where to go...he just said "Lets go somewhere." Pretty soon the horse wasn't even interested in the gate. That's because the rider showed her that there was nothing to be scared of....she could trust him and he understood her unconfidence. This is how the rider showed his horse leadership. The reason the mirroring works is because for unconfident horses, when we aren't in sync with them it adds to their tension...the lack of harmony is bothersom. So when we get so in sync with them, even in our head movements, the horse feels that harmony and the lack of disharmony calms them down.
Now, on the other end of the scale, you have the horse who is not unconfident and is being very left brained and is arguing with you. But you still have to ask yourself "Why is she arguing with me?" It's usually because the horse is bored, the rider forgets the horse's motivational needs, or the rider gets direct lined and focuses on their goals and not the horse's needs. And when the horse protests and the rider gets forceful, the horse protests harder, which is what you experienced when you said "Screw Parelli." Now whether that blow up was from unconfidence or just dominance, idk, I wasn't there, that's what you have to figure out. So in this kind of case, the worst thing you could do is fight her. She will just fight back. Hard. And it will ruin your relationship. So again, it all starts from the ground. Make sure your play session is VERY interesting and provocative. When you get on make sure you are in the right frame of mind, which means that you are not putting your goals before her needs. Now it's your job to make things FUN! Keep things interesting and don't dwell on any exercise....once she has the idea MOVE ON. She might just be saying "This is boring! God why are we doing this again?!" Do you have the Parelli Patterns? If not I would get them. They are awesome! If you can't get them, just set up some puzzles for her to figure out....figure 8's, a weave pattern, etc....you can also work on getting your yields (hind end, front end, back up, sideways) closer and closer to true Freestyle, which is bridleless. Follow the Level 2 riding tasks.
Really, gate sour issues can be prevented with proper preperation. It's really an issue of the relationship....whether it's a lack of trust or a lack of respect, but either way it's OUR fault when gate sour issues pop up. My first Levels horse had a bad gate sour issue for a time, but once I got more into the Program and knew what to do, the issue went away because I was more informed for the needs of my horse. Once I got MYSELF in check, the issue went away. How interesting :)