Just wanted to add, that the 'belly button stick' thing I described, is the sames as what skyseternalangel has been telling you about longeing. It's just another way to think about your body positioning and what really made things clear for me, when I was learning proper body language. Longeing on a line and free longeing should be executed the in the same way, the only difference is when free longeing you have to use your body language to control their head, since you don't have a line to them. But being in a roundpen helps that, as they are unable to 'leave' the circle.
I disagree about you not being ready to free longe. I would rather I (or someone else knowledgeable) could be right there to help walk you through it and help you with your timing, rather than you having a go at it by yourself the first few times. Simply because you have to be more clear and sure of your body language than you do with a line to their head. Which is why I think it would benefit you so much.
I'm worried that, while your trainer seems to have more knowledge than the past ones and may be a good instructor, she may not truly be as effective as a horse trainer as one would hope. I don't like to hear of people keeping a young horse only at a walk or trot. Horses need to be taught to move out forward freely at all gaits, loping needs to be part of the ride, from day 1. Does the trainer only do trot work?
If your horse were with me in training, I would have her covering ground and doing a job (learning to work a cow, work the flag, rope the sled, drag a tire, turn a barrel, trail obstacles, etc etc), getting her broke in the face, then the neck, then shoulder, ribs, then hind quarters, while performing those jobs. You would probably not even really be able to see me working on that stuff, without looking very closely. I do not like to drill young horse. I like to give them a job, that allows me to work on that stuff, almost without the horse realizing I'm working on it, because they are focused on the job at hand.
It concerns me, if she's only doing trot work. That's really not getting your horse worked like she needs to be. Horses can trot all day long... if you ever watch herds of wild horses covering country, they are always in a long trot. You will never see them loping, because that takes a lot more out of them. It really looks like your horse is feeling pretty fresh in the videos, like she really isn't getting worked as much as she needs.
The same thing I told you about overdoing something, applies to the halter situation. Your mind set needs to be in the moments. When you work with her on something, see where she is at THAT DAY and look for just 1% improvement from where she started that day. When you get that, quit. Don't keep pushing when she does something well, because you think she can do better. That mind set will lead you to pushing her to say no. Try to get in the habit of approaching each day fresh, gauging where she's at that day, and looking to just get a little bit of improvement on that. A slow, steady increase of improvement where you and your horse continue to grow more confident due to little successes, will pay off more in the long run, than two days of lots of improvement, followed by a day where you push her too far, she pushes back and you two get in a fight, pushing you back quite a ways in the improvement and the confidence departments. Try to set both of you up for success. It is feasible to expect to be able to improve 1% over 100 days, but it is not feasible to expect to improve 100% over a few days.
Your horse most definitely remembers the work you do with her, so it does you a lot more good if you get a little improvement each day, and can start each new day a little bit ahead of the day before, than it does if you push her to the point of a big battle, and you have to keep having days where you start way behind where you started the day before.
Remember the tortoise and the hare! Slow and steady wins the race ;)
For the biting thing, you're just going to have to be quicker. She obviously has to get her mouth close to you to nip or make the gesture, so that is the moment that you have to make contact with her. If she is pulling her head away, you were already too slow on the correction. You have to think ahead of her, so that when she reaches over to do it, you are ready to correct right then before she gets a chance to pull away.
I didn't really get a chance to watch the 2nd video very closely, but one thing I did notice, is that your horse gave lots of warning that things were escalating before she tried to run you over, and then rear. Every time you stopped her, coming toward the camera (toward her pen, I think you said), she didn't stop with you, she kept going. That was her pushing the boundaries and telling you she wasn't paying attention. If you stop and her feet even so much as go one inch past you, you need to immediately lay your lead rope or whip across the front of her legs and make her get back. I feel if you had corrected her the first time or two she did that, it would not have escalated to her thinking she could barge past you.
I agree with your assessment that she was kicking out at you, with bad intentions. That is where I would have very forcefully slapped her across that leg with the whip. And if I didn't have a whip, I would've immediately run up my lead rope, to where I was right next to her barrel, got short control of her head and gave her a good kick in the underside of her belly (all of that would've happened so fast, otherwise the timing would've been off and ineffective). I don't know that I would want you doing that, because it requires you to be incredibly quick and confident, and you have to have yourself in a safe spot, with control of her head, so that she can't kick you if she decides to put up a fight. I would rather recommend that you carry a whip with you at all times, until you have her where she will dependably comply with you, with no fight or lashing out.
I'm really glad you've made these videos. It takes a lot of guts to put yourself out there and subject yourself to critique, but it is what is necessary if a person want to really improve. Not only is it great for us to be able to actually see what's going on, it's really good for you to watch yourself as well. Never stop videoing yourself. I still video myself about once a week. If nothing else, on days when I'm feeling down about myself, I can look back at an older video and see how much I've improved.
Take some pride in knowing that every single one of us, feels your horse and you are doing MUCH better, than what we previously thought based on your posts. I think you have a pretty good, natural sense as to how to handle a lot of things. Have more confidence and trust in yourself. Try to stop overthinking things so much and go will your 'feel'. I think you (and your horse) are more capable than you give yourself credit for. Plus you have the most important quality, that many long time riders don't, the strong drive to improve and a willingness to try just about anything to get there. I really see a lot of potential in you and wish you were located somewhere near central California, so I could give you more hands on help with your timing and some of the things you are having some real trouble with.