I think it’s a pressure issue. Like the mare is pressuring herself up about what is expected, and in turn much like a blown up horse if she is not already one. I don’t think it relates to any disrespect on her part, it’s just in her own head, and in a way on you for letting her get there, although some horses go there really easy.
I don’t know that gate issues are something you necessarily overcome, because once you go in and compete the pressure is immediately back on. I think they are something you deal with rather than fix I guess.
I do however think it’s really important to do other things. Like
@My Salty Pony said, do something else. The horse already knows the patterns. Go outside, keep her fit and her mind working on other things. Too much arena riding is never great for a performance horse in my opinion. At least vary the arena work you do if nothing else. If cows are available cut, sort, rope, whatever you want. That is different than what you are doing, as it’s a whole other thing for her to think about.
I have had a few successful barrel and pole horses. One was pressured up and blown up. She enjoyed the events I believe, but she took it very seriously and couldn’t quite handle it, and the others were all calm about it. It’s a personality thing to me, and working with said personality. In any case, I didn’t run patterns almost ever at home, there is not really a need once a horse knows. Sure, I’d have them do some exercises on occasion, but I didn’t run them excepting once two days prior to an event. Sometimes not even then.
Even the blown up mare it helped. She knew she wasn’t running a pattern or being intensely trained on when she went into the home arena. She went in perfectly fine. She was a good cutter and decent team roper, but in the team roping she could pressure herself up there too, causing box issues. She was hotter than hot, and pressure was why she was blown up to begin with.
Yet, no matter how good she was at home, she would pressure up in town. I think the solution would have been to take her a few places and not run when she went into the pattern, but the second I ran her she would have pressured up again. So, I just dealt with the gate issues, and she was extremely competitive. Overall I thought she was very happy about it, but she pressured herself at the time of entering and running. It just was what it was.
Now, I could tolerate it with her because it was her personality. I have seen horses blown up at the gate that seemed like they didn’t want to run, and weren’t even competitive. If that is your mare, then why make her do something she doesn’t want to do? Buy something else to compete on that actually enjoys it, and do something with the mare that she enjoys.