Hi there Jess, welcome to the forum!
I am not sure, as it wasn't clear from your post, but what makes you think that her behaviour could be attributed to being a mare? I.e. is it something to do directly with her cycles or does her behaviour change obviously around breeding season?
Purely going by what you have written, she just sounds like a badly behaved horse, regardless of gender. Seems to me that she might have a slight case of agoraphobia for want of a better term. If she only does it in the field then I suspect that she is concentrating on her environment and wanting to react to that, rather than the commands you are giving her.
I would start incrementally - work her until she is composed and thinking straight in an area that she is comfortable in. Then take her out into the field, perhaps just for a walk on the first day. Keep her focus on YOU, not on her surroundings. Of course she can look around (within reason) but she MUST be responsive to your commands. Practice exercises just as you would in an arena - spirals, serpentines, leg yielding, anything that keeps her mind occupied. Then move up to a trot. Same thing.
When you have the walk/trot exercises down pat with smooth and willing transitions, then move up to a canter.
If it makes you feel any better, I have dealt with many a horse that matches exactly your description (mare, gelding and stallion) and it just takes time, work, patience and consistency. Organise your workouts so that everything is a progression, rather than introducing too many new elements at once.
Good luck and keep us posted.
All horses deserve, at least once in their lives, to be loved by a little girl.