Lots of horses buck on the lunge when they’re fresh. Most hunter people don’t really train horses to lunge as a tool, they use it TO get the bucks out. So even some dead quiet horses will think “time to get the fizz out” when you attach the lungeline.
Also how are you asking her to change direction? Do you have one of those Y connecter things? A lot of people don’t lunge that way. When they want to change direction they stop, have the horse stop, walk the horse to them/walk to the horse, clip the lunge to the other side of the bit, and send the horse back out. So if you tried to revese with you inside the circle just turning her around, the horse may have had no clue what you were asking and reacted to being confused. I’ve seen NH types turn horses around without bringing them in first but most hunter people I know don’t do it that way. So, again, you may have been throwing yet another new thing at her on top of all the other changes in her life.
I’m also a little unsure about your level of experience, OP. It might help a little bit to know HOW green you really are. You said initially that you never really had any lessons. So if you’ve just been kind of going on intuition your whole life/learning from watching videos/just getting along on completelty made horses without having to actually learn to RIDE or TRAIN-- it’s not surprising to me that this green horse is showing a bunch of holes in YOU. It’s also ok if you don’t think it’s any of our business-- it’s just puzzling to me in trying to put together the pieces of what’s happening here because in some ways you sound like you know what you’re doing and then in others, not really. Everyone has to start somewhere, so it’s not meant to be a criticism. But what you can/should do with a new green horse is going to depend on YOUR level of skill.
Also, my goodness, you continue to throw a lot at this horse. You’ve had her just a handful of days, if I understand the chronology. She’s lunged on the line, free lunged, gone on a walking trail ride, gone through the jump chute in the round pen, been jumped in the ring, been free jumped in the ring, been ridden in a pasture (?), been hacked in the ring… all in a new place while she’s adjusting to a new rider, new handlers, new turnout situation, etc. This is not what you can expect a normal hunter horse to do over the course of a couple days. Not that hunter people NEVER do any of these things, but we don’t typically throw all this stuff at a horse one after another. So you’re really pulling the rug out from under her if she’s used to a situation where someone comes out and W/T/C in the ring 5 days a week and jumps in the ring one additional day.
Regardless, this is not a dig on you, but you need help. You keep having surprising/bad experiences with this brand new horse-- time after time after time. Where is your trainer?
