If it's only in the English then i'm thinking saddle fit may also be an issue or that your balance is lacking in an english saddle.
I'm also very against a tom thumb bit. I hate them really. It is THE worst bit in the world in terms of balance of it's construction. A horse that works even halfway decent in them deserve a gold medal. I've demonstrated on my own arm to friends why they suck so much. I stuck the bit in the crook of my elbow and applied maybe 2 ounces of pressure to the left shank to 'turn'. The link pinched so bad I had a purple bruise for a week. Not only that but when you pick up on one rein that shank wants to twist and push into the horse's face, thus putting pressure on the side of the mouth like a snaffle. All of that aside the straight shanks do nobody favors, it doesn't allow for any signal before the bit comes into play and it's single joined creating a nutcracker action.
There are many types of snaffles to try and that is the type of bit needed for basic work like this. Mullen mouths, single jointed, double jointed then of course all your different cheek pieces, all of which have a slightly different feel.
Curb bits aren't meant for more whoa, they are meant to refine cues on a horse that already has a solid foundation. I can't make you change bits though so if you insist on using a curb either of these is a much more kind option:
I prefer a curb that is not jointed. However this one is hinged so your shanks will still move independantly. The port is just high enough for tongue relief and be very very mild. The short swept back shanks do not offer much leverage and give signal before the bit is engaged. Western SS Low Port Futurity Bit - Statelinetack.com
My second choice for a curb bit:
This is double jointed, making it more mild and again has short swept back shanks giving signal beforehand. This bit can work much like an english pelham in that you can attach two sets of reins so you can primarily work off of the snaffle and only use the curb when needed. Western AT Copper Dog Bone Ring Argentine Bit - Statelinetack.com
Even a barn sour horse will show a tendency to want to be in one area even in the arena ( the corner closest to their turnout or such). That is where you can begin to work on her issues. Like I said in the other thread, make that area an uncomfortable place to be and the rest of the arena easy.
On your walks, make sure she does have a couple feet of lead and you aren't leading by the clip.
Although, once things are good in the arena, the trails should be much better and if you have problems you can always bend to a stop, get her to relax and carry on.
I think I recommend this in the other thread as well, but at first you'll want to work her at the barn beforehand and afterward just to reinforce that coming back to the barn quicker is not a great idea.