I also don't care for the dually; I would probably only use it as a very last resort if a rope halter, or even a stud chain did not work.
I would definitely start teaching her to back out of your space. Teach her how to disengage her hind and front ends, so if she starts getting snarky, you have a way to control her body. Teaching her how to longe will help you teach her how to work 'outside' of your space, and can be a good tool when she just has too much 'foward' when you are walking with her. If she wants to go, then make her go; in constructive circles around you.
I would carry a crop, carrot stick, or dressage whip with you so you can cue her easier.
For the gate leaning, every time you go to the gate, use the carrot stick, or crop to make her back out of that area; and tell her 'back off', so she learns a cue word to the action. I would go out to the gate frequently JUST to ask her to move away from it. The more she does it, the quicker she will learn that the gate is part of your personal space, and she needs to respect it.
When you try to take another horse out, have a partner; have that person lead the horse in and out, while you enforce her 'back off' cue. She will learn quickly.
"The ideal horseman has the courage of a lion, the patience of a saint, and the hands of a woman..."