Barn sour

I think you are doing the right thing by circling her every time she speeds up when going home. As for her moving around when going away from the barn - you could also try circles or making her move even more laterally. Anything to get her attention on you and not where she is.

Also, don't always get off by the gate at the barn. Get off somewhere different each time so she doesn't associate the gate with the end of her work. Or perhaps go through the gate and do some hard work near the barn then some nice quiet walking away from the barn. It's the whole "make the right thing easy and the wrong thing hard" sort of thinking.

I'm rambling, perhaps someone else can come along and give you some better ideas.

Agree with MM. Lots of circles when she doesn't listen. You may get dizzy from it but in the long run she will get the idea that she isn't going to get her way. Maybe even dismount away from the barn and walk her to it. Barn sour horses are a lot to handle at times and a lot of work for their rider...But it sounds like you have a good handle on it..

Maybe you can try doing some lateral work with her? Ex; leg yielding, circles, ect. Personally one of my favourite exercises is getting the horse to leg yield on a circle slowly making it bigger and once you have a nice tight circle get them to leg yield out.
I find with horse's with separation issues and being sour often if you keep their mind occupied (which is why i find lateral work is great for!) they usually have less time to think about fighting you.

Excited to see your video

H4L, you shure do use some big words. hh I will try to respond to your comment. If she is accelerating and I do not respond with nothing, she will run to the barn, and then if I let her run, it is hard to stop her at that point. As I said she does not have that much respect for a bit. Maybe some other people would put her a bigger bit(I ride on a simple snaffle), but I am a no no for that. I want to dich the bit at some point. I don't want nothing to be done by pain. I ride her bareback for now, I use saddles only if I am going on a trail or will do canter/gallop. We don't do much trot either, as I am trying to make her go home as calm as possible. She does slown down or stop when I lean back and say a word that I use for stopping and she will stopp, but will not use that signal for slowing down. Also she does not react to "yielding", or my leg pressure, that is something I would have to work on really hard, because I know how much it is important, maybe a stick would help?! I know that seems like "what a hell did you teach that horse if she does not know even basics?" But really I am not that type of a person who is affraid of admitting that they did wrong. Most part I blame my dad for her, because she was our first horse(10 moths when she came- now 11 yro) and he did the best way she knewed. It is not an excuse for me. I just hope a older horse can be restarted?

Oh she is stubborn horse that is for sure. I like what you said abut changing her opinion so that she thinks her way is my way. Also , you might be right about the bit... The thing that I know is that bareback is not part of the problem, because she does the same way being saddled. Trust me. I am not saying I am a "good rider", but I really do know how to balance my self bareback, I learned how to ride bareback long before I got to the saddle. It does take a lot of time, but as I sad she will be my horse as long as she is alive, I will do my all, to make her as best as she can be. For her own good, not for mine. Ridng is not that important to me, when it comes to horses. We did the work again today, I said I would make a video, but everyone was "buisy" so no one could film me. I done some of the thing suggested like working har by the barn, although it is mud, I did work her, little bit of a trot and that was enough because mud made it more difficult for her, I done it twice and bring her back to the field, third time she was going home calm. :D jeejjj Flexing her is making me nuts, she will bend her head on the left side, but wont give up on the right, she is very stiff on the right side. All in all we made a good progres today, and I am happy with my girl.

Try making her go backwards in the direction she wants to go, then she will have to think about it, turn her around and if she rushes again just keep doing it:)

Progress in small steps is always the best. some horses just do not get it. and we need to allow them to understand what we ask of them in small steps. 
sometimes circles work other times like lordd has said going backwards works. and  i have taken them back out away from the barn and than turned them in circles and started back towards home. as soon as she gets jittery and you think and feel she is getting uptight than turn her and go away again. after a while she will realize that going home at your pace will eventually work. 
this could take days for her to figure out. so do not try to accomplish it in one or two or three lessons.  and when you circle,just a note. if she is stiff on the right than make her go to the right, 

She was naughty today at first. Jumped twice going back home, like a goat on all four
Later we went outside the field to the road, she was hmm ok I guess, not the best, but not the worst. Well there will be a lot more good and bad days, but I enjoy spending time with her every day for a change(until now I have been mostly riding my studs-they seem to be much more cooperative :/) She is great when riding trails with other horses, and riding in pairs, she is like a dream, but when I go riding myself I usually take the boys. No more cutting corners, will stick with her until she improves.