Without being there or knowing her bodylanguage, don't know whether 'antsy' was fear or attitude, but considering she's new to you lot, I'd guess fear. Sounds like people have just gone too far, too fast with her.
It's unclear whether the trainer got to know her/asked anything of her prior to saddling, but I would have first, establishing basic behaviours & ensuring she was good with it. If she was 'antsy' to be saddled, I wouldn't have asked for more until she was fine with it. *Also worth double checking it wasn't the tack or her back that was the problem. Once I'd got her fine about saddling, then I'd saddle her up & teach her to stand for mounting. If/when she was 'antsy' I'd work through that before actually getting on too. Probably by the time she was in sight of the pasture, it had reached the final straw & she just snapped.
She was lunged and proceeded to try and barrel kick the trainer who luckily saw it coming. The trainer corrected it and her behavior got a little better although it is obvious she doesnt like the trainer after their bad experience.
Again, without more info, don't know why she's doing this, but I don't think she would have taken a strong 'dislike' to the trainer if she understood the lessons & 'correction' was clearly understood. So I suspect again it was fear based. What was she being lunged for? Has she been taught to lunge & other 'groundwork'? Again I'd start at the beginning & slow down, try not to be confrontational about it.
Oh and one last thing she really likes her butt scratched and often completely turns her butt on you and I find that it is just bad manners
I once had a horse I inadvertently trained to do that, because she loved a butt scratch so much. She's doing it because this behaviour has got her what she wanted in the past. So you have to a) make sure it never, ever works for her again and b) I'd also make it unpleasant for her to do - I'd give her a smack on the behind whenever she tries it - with a stick/whip or such, because you need to keep out of the way of those hooves.