She is not working through her back; she is ducking her head and her back is very hollow; mainly because her head is behind the vertical (as you know) and not correctly bent. How to fix? She needs to move INTO the contact, not hide from it. Throw the reins away, I mean--ride like she's a western pleasure pony! When you turn, use minimal aids--she may be 'hiding' because of previous harsh hands (there's one picture where your asking for some headset and she replied with putting her nose on her chest, hehe)--also, put her in a snaffle, or better yet, a hackamore. With no headset, start to push her forward; you need to feel energy in every gait, but it must be CONTROLLABLE energy, not 'omg, we're running awaaaaay!' energy, hehe. Work on long straights, circles, and some side passing if you don't need a lot of rein pressure to go sideways. Horses 'suck back' sometimes because they're not thinking forward.
Once she starts moving for you, start trying to ask for just a little 'collected' work, but DON'T expect her to be on the vertical. Beginning level dressage horses should NOT have the headset of Grand prix horses! Just ask her for a little bend, and if she sucks back, puuush her into your hand--ride from the rear end, into your hands. After a bit of collected work, ask her to stretch down long and low for you--the true test if a horse is trained correctly in dressage! Most of your time should be focused for a week or two in CORRECT long and low frames; the correct long/low teaches a horse to lift it's back and move CORRECTLY, not just with a headset. Then you can slowly start to ask for more and more of a correct bend.
The reason she's behind the vertical is because of improper dressage training; they trained a headset, not a way of traveling. She is VERY cute, seems like a cute mover, and that has carried her thus far... but if you start to do some correct work, some shoulder ins and some haunches in when you start asking her to bend her head into a nicer frame, I think you'll be shocked at how much nicer she'll be when she's REALLY working through the back. She looks like she has a lot of potential!
If you have any more questions, just lemme know. I looove paints, and love seeing them in traditional english disciplines, like dressage and jumping (I'm a western pleasure/HUS girl, myself, with some solid dressage foundation!) Good luck!