Since you failed to mention in your original post that your horse has been cleared by the 1) vet 2) chiro 3) dentist and 4) farrier, there is absolutely nothing wrong with us asking if your horse has any soundness issues. We can't read your mind. We don't know your background. And we always certainly want to make sure in any discipline, that a pain issue isn't the root of the problem, before you go and drill the horse on training.
We can't just assume details about you. Assuming gets you into trouble on here. That's why we ask questions. It's not a put-down of your character, so don't get defensive.
Now, as far as the speed issue and the "throwing shoulder" issue. Do you have a video to show us exactly what you mean when she throws a shoulder?
Tell me if my description is correct (or if I am way off):
--As you approach the 3rd barrel, your horse wants to turn too soon and anticipates that she will turn.
--To prevent her from turning too soon, you direct or neck rein her to the outside.
--This causes her shoulder to be thrown inward, and causes you to either hit the barrel, or it causes her to cut it too close, and you have to finish the turn really wide.
Is that what is happening? If it is, I'll explain how to correct it. If not, please explain further about what is happening, or have someone take a video of it.
Or....... when you approach the third barrel:
--Is her nose bending nicely to the inside, but her shoulder is popping to the outside too much, and thus she's "spinning" her hind end around her?
This is where a video would help because there could just be something small in your riding that we could fix, if we knew exactly what was going on.
It may help for you to check out a few free videos on YouTube. Dena Kirkpatrick has a lot of good ones. Here's one of them to get you started. This video shows how important it is to have good bend in a barrel horse (since you stated she has bend for dressage, but seemed to think bending wasn't as important in barrels???)
I agree with the others that if you are having any sort of issue on the pattern such as this, you do NOT want to add speed at this point, or you'll only make the issue worse.
Once you get that perfect pattern back at the lope, then you can think about adding speed.
I agree that breezing a horse is the best way for them to LEARN how to run. And even if she breezes in a wide open field, it usually takes them TIME to learn how to run in an arena with fences. You certainly don't want to force a horse to run with spurs, whips, or otherwise, as that'll just make them resent their job. (Not to mention that spurs are used for lateral movement and refinement, but should not used for making the horse "go faster".) But sometimes it just takes time for them to figure the speed part out.
And one question I have: Are we talking about an English Tom Thumb or a Western Tom Thumb? Because there is a difference. Can you post a picture of the bit you are talking about?
Because if you are talking about this one:
That bit is good for nothing except a coat hanger. I completely disagree that:
|This bit is only bad in the wrong uneducated hands.|
It is perfectly acceptable to have a separate bit for dressage and a separate bit for gaming. It helps the horses to tell the difference to have a tack change. I do the same for my barrel horses, when I take them to local shows for western pleasure, reining, and competitive trail. Or when we are just plain trail riding. Or when we are competing, versus schooling at home. I use different bits based on what I am doing.
A longer shank doesn't make a horse's mouth hard. But harsh hands will. A longer shank should actually allow you to be even softer in your cues, because very, very little movements will send a signal to your horse. That's why you seeing reining horses with these super long shanks -- the rider barely has to even shift their hand position for the horse to instantly feel a change. Talk about softness!
You can try a little S hack if you want, but they tend to make horses a bit stiffer. Based on your descriptions thus far, it sounds like we need to get your horse more bendy -- not stiffer.
Any of the bits SorrelHorse mentioned would be good ones to try.