I'd get everything checked out of course before calling it a behavior problem. When is the least time she's had an adjustment or had her teeth done? If it's just when she sees something out of the corner of her eye i'd get her eyes checked too.
What mouth pieces and cheek pieces have you tried on her?
The martingale is just a badly put on bandaid. Right now, the two of you look to be in a big pulling match, she's running around on the forehand, not being soft in the face at all and you're leaning back at times and looking to be putting a good bit of pressure on her to keep her in a frame.
Now keep in mind I am coming from a western perspective but all of my horses are trained to ride on contact ( eventually) without being on the forehand, behind the vertical etc.
I'd take her back to the beginning, she just really doesn't look like she has a clue how to respond to two reins and i'm going to take a guess that she isn't the softest off of just one?
I introduce contact about two months into a horses training. Before I introduce contact, that horse is butter soft everywhere. There is no resistance to one rein at all and m horses move off of just a touch of my calf, whether it's moving their shoulders, rib cage or hindquarters, my horses also rate off my seat. The next step is introducing the correct response to two reins, I introduce it at a halt. I will flex my horse a couple times first and I want a correct flex. I don't want the horses nose cranked to the side, if it takes more pressure than just closing my fingers on my reins or starting to take the slack out, the horse isn't prepared yet. When that is good I take the slack out of both reins and wait.
In the first couple lessons I just want the horse to give, whether it is a downward motion or breaking at the poll, anything that creates slack in my reins without head tossing. From there I get pickier and want flexion at the poll without the horse hiding behind the vertical. Next is that I hold that till I get a correct step back, I will hold till I get a step backwards and feel the shoulders lifting as the horse steps back while maintaining softness in the face.
I spend a couple weeks perfecting a backup before I move onto a stop from a walk( first time I use two reins while the horse moves). I pick up, just as softly as I do when backing and wait until I feel my horses back raise and hindquarters step under to a stop. I'll then back a couple nice correct steps.
I'll then do this for a couple weeks, progressing to a trot and lope. When my horse is riding into the stop very well I introduce contact.
At this point i'll take the slack out of my reins and my horse will start to come back to a stop, when my horse starts to come back i'll cluck and put my calf on. At that point my horses will then push forward off of their hind end and i'll keep a soft following contact. Some horses will raise their head and others will tr to suck back, i'll keep that soft contact, cluck and use my calf till I get one excellent stride where I can feel my horses back raise, my horse track up nicel and be soft in my hands, then i'll let that contact go and go back to riding around on a loose rein. I get that first stride perfected before adding any more.
So, it's quite different than how an English horse is trained but it has worked very well for me.