My boy sounds a little similar. He can be extremely soft on the bit, then soon as he gets in a bad mood he's pulling my arms off. I have tried various bits to see if he was happier or less happy in them. Tried harsher, softer combinations, gags......honestly nothing changed it, he pulled just as hard in all the bits. The harsher the bit the more he just cut himself up (Sores under shin strap and corners of the mouth). So I stuck with simple. The only thing I could do was to do all I could to keep him from getting frustrated or pissed off at me. It took a lot of time to work on avoiding the fights.
I suggest only fighting with one rein as well, if they get hard on the mouth when you apply even pressure on both reins is to pull up and back with an inside rein and dig your inside heel in. Keep very light pressure on the outside rein. You want to tip the nose in but not over bending. Soon as the horse relaxes into it, give slack in the reins and continue as if nothing happened. This is honestly taking away all the fight out of my horse. At first he fought this method, but I just held firm and now when he starts to be a pain in the rear on the bit, I'll raise the inside rein, put leg pressure and he softens up quickly.
As fore the pulling back, the wonder bit (the one pictures above) has a curb strap on it, which makes it harder for the horse to spit out because it is restricted from moving up. She could be feeling constricted in the mouth and it could be hitting her lower teeth. This is the most plausible explanation I can think of. Try removing the curb strap first then the bridle and see what happens. Otherwise she is being headshy / having general bridle problems.