Wow, sounds like you have a lot going on. It appears, through no fault of your own, that your mare has some pretty big holes in her training. I want to encourage you to keep working with her, you can work this out. My appy was unridden at 8 and has been a major challenge as well. They seem to have the ability to think up new evasions as quickly as you fix old ones. Their are two old sayings I like about appys: Why don't Cowboys like appy's? Because they don't like a horse that is smarter than they are. AND Why did the Native Americans use appys for their war horses? Because they were so mad from training them they were ready for a fight.
If you don't have a lot of experience, you should really consider getting a trainer, or at least using a trainer for some of the things I'll offer below. Some of the suggestions I will make require quite a bit of experience or can really mess things up more. Just so it's out there early, remember horses learn from the RELEASE of pressure.
Appys - in my experience, appys often move into pressure when scared. This is different from most other horses, and if you don't expect it can be really dangerous. For example, with the farrier, my mare would leap forward kicking rather than pulling back and away.
1) ground work - lots, and lots, and lots of ground work. Not just lunging her on a circle, but walking on the trail, going for hikes, down the sidewalk, into town, teach her to jump over barrels from the ground. Teach her the 7 Games and to yield the four quadrants (hips, shoulders). Build your respect and trust on the ground.
2) Become an expert at the One Rein Stop. Learn how to grab one rein and spin her around. These are your "Emergency Brakes" when she flips out. You wouldn't drive a race car without decent brakes, so put brakes on her. You need to train her how to ORS and Ruffian referenced it above ("pull her head around and don't let go until she comes to a complete stand still")
3) Consider leg restraint training. I have used hobbles and leg straps with great effectiveness on my mare. Essentially teaching her that she needs me in some situations and can't just fight her way out of everything.
4) I don't like riding in the horse's regular pasture on a green horse. That is "their" space, where they get to act out and be free. Just my opinion.
5) "Won't let me get back on." Not exactly sure how she is evading here. My mare would just put it into reverse whenever she felt you starting to mount in the field. Again, you have to be the rock in the ocean (sorry for the Zen reference). Walk up as though you are going to mount. If horse moves, move horse's feet with energy. Get their mind back on you. Make them hip yield, or shoulder yield (see where that ground work helps) until they are breathing hard, then calm everything and start to mount again. Make the wrong thing hard (moving on mounting makes him move my feet around and get tired) and the right thing easy (if I stand still, he doesn't move me around). I also think it is important in this training to sit on the horse a few minutes without asking anything once mounted. Teach the horse that getting you on their back doesn't instantly mean start moving your feet and working. Teach her to stand with you up there.
6) Barn sour - a frustrating habit for sure. There are lots of ways to train for this, but I really like what David did in this video.
7) IMHO, training her more in the arena and round pen will not help with making her a better trail horse (except that it will help put the foundation there). As Ruffian indicated, only trail rides will help, but you need a better handle on this horse before you go out like that.
8) I saw that you had another thread on which bit to use with her. Not sure what you ended up with, but you should probably be in a snaffle with her based upon how green she is. I use a Myler Full Cheek Jointed Snaffle (MB02 I believe) and my mare loves it. I'm now training her to take a curb (also a Myler). Her evasion for the curb was to rear over backwards onto me.
9) IMHO, you cannot control a bucker with a halter, and particularly with a webbing halter. Look at the video of PP at Road to the Horse, even he couldn't ride that horse in just a halter (not that I'm pro- or anti-PP, he just has way more experience on horseback than most). You need to get her to accept the bit. Ruffian had a few suggestions on how to do this, but none of this worked with my mare. She hates anything going in her mouth (worming paste, bits, etc.) so she wouldn't even taste the "nummy" she would just react away from the attempt. When my mare began refusing the bit, this is what I did. a) you need time and patience; b) put a rope halter on; c) stand where you would to bridle, slip your far hand around her jaw and hook your thumb under the rope halter. In this way you move when she moves, up, down, anywhere. d) bring the bridle up and ultimately hook your fingers through the off-side of the bit (so now my right hand is hooked by the thumb to the halter and the index and middle finger are in the off-side rings of the snaffle). Follow the horse as she evades. Be calm and patient. You wait until she stands and relaxes. You are like a piece of ribbon on her halter, you follow her where ever she goes. e) push my thumb into her mouth between the incisors and premolars (in the diastema) and wiggle it on her tongue until she opens her mouth. f) slide in bit. g) complete bridling. Repeat over and over until she doesn't react.
My final word of advice is you have quite a few things to work on, and you can't do them all at once. Get a plan as to how you will address each issue and take them sequentially. I've tried, based on your OP, to put this in the order I would address the issues (but I'd work on the Bit/bridle issue earlier). You can't effectively ORS with a halter. Good luck!