A lot of your problems have to do with going forward. Horses that have a problem with their go button back, toss their heads, go sideways, and worse, rear.
Get a dressage whip (cause they're longer) and squeeze your legs. When she doesn't go forward (marching like she's going to the feed bin, not like she's a drunk wobbling around), use the whip. Do NOT kick and do NOT just squeeze harder. You are teaching the mare that when I squeeze lightly, you must go forward.
Don't hold her head at this time either--you want your aid to be clear.
Now when she wants to rush back to the gate... fine, let her. Don't fight. But WORK her at the gate! Circles, backing, loping, etc. then let her rest at the other side where she is the worst about cutting in. Let her stand there and think about how awesome it is. Repeat.
Never get off of her at the gate or at the barn. Dismount in places where she doesn't like to go because it's too far from the gate/barn.
If she ties, you can tie her in the stall when she returns so that she doesn't think her stall is that awesome.
Take her out of the arena and work her by the barn if possible. This will also reinforce the idea that the gate is not the be-all-end-all. YOU have taught her that, even if accidentally.
Don't get angry--when you get angry, it only reinforces the idea that her stall is awesome and you riding her sucks. Give her breaks and tons of pats when she does even the little things well. She'll come around.
Dressage in Jeans
- My blog with dressage tips for happy, relaxed horses, specifically for those who ride dressage in western saddles, no saddles, cowboy boots, or jeans. ;) Also now with cute pygmy goat pictures! :P