Hmmm, she sounds fun! Seems you have a feisty one!
Without being there, I'm only guessing, but... I think your trying to get her to trot originally may have confused & alarmed her, but she then perhaps decided you were playing with her & started playing back. You probably realise that she won the game when she flipped her head at you when you got to the paddock??
I would start her as if from scratch, getting her to yield to pressure with halter, hand, lead, stick.... Make everything easy and rewarding for her to get right, so the right behaviours(& attitudes) become more likely. Try to avoid confronting her until you've established some good stuff. Once she's got the basics going OK & has learned that it's worth her while to keep you on side, then I'd suggest a kind of join up thing.
Use the small paddock you mentioned to play with her in, then if she gives you any attitude, drive her away forcefully & work her a bit. I'd use a lunge whip or a stick, rather than just a soft lunge line, so that you can create as much pressure as needed to stay safe. Whenever she softens, quit the pressure & walk away. If she comes to you nicely, invite her in & reward her for it. If she comes at you with her ears back, drive her away again. Pretty soon she will decide it's worth showing you some manners.
I much prefer to work with a horse in the open generally. It keeps me on my toes, because if I'm not doing the right thing at the right time, the horse will just leave. Likewise, a pen with 70cm fence sounds great for testing your skills in this way. However, until you establish some willing control over her, she just won't want to be with you if you try to push her. Driving her away won't work if you're not in an area to keep it up, unless you're super fit!<G> I don't know what the problem with a rectangular yard is, altho a little smaller would make it easier to start with. If you've got a hotwire, it would be the easiest way to divide the paddock.