This doesn't really sound like a "go" horse to me. The horse walks on a loose rein and doesn't try to trot? And canters without trying to gallop? Plus is quiet on trails. So it sounds like you have two gaits you can ride on a loose rein without the horse trying to go faster.
When a truly hot horse gets ramped up, even when under perfect control they are "asking" and looking for a signal to trot from the walk, to canter from the trot, and to gallop from the canter. And to gallop faster from the gallop.
Are you sure the horse doesn't just have a big trot? A lot of Thoroughbreds have big, energetic trots. It can be physically difficult for them to balance at a slower gait. Especially when getting older and maybe having arthritis or other issues.
What you consider a fast, out of control trot might be this horse's working trot and actually the pace where she can relax. Asking her to go slower may require some balancing and strengthening exercises before she can accomplish a slower speed. She may not be fighting you, but rather trying to find balance from the reins when you ask her to slow down.
Racehorses are often trained to use the snaffle for balance.
Is there a pace where she likes to stay consistently at the trot and finds a good rhythm? You may need to learn to balance at that speed either by posting or two-pointing, especially if she has a choppy trot. Where she is comfortable may be faster than other horses you are used to, especially if you ride stock horses.
It may be helpful to lunge her at the trot and notice where she is the most comfortable. Then imagine yourself riding this speed and think about how fast it would feel. If she can jog easily on the lunge, then consider that you may not be comfortable at the trot and giving her cues to speed up by gripping without realizing it.
I wouldn't worry about if she can handle a fast trot at her age. Many horses can easily trot for hours when in shape, up into their thirties. Many retired thoroughbreds go out for gallops well into their late twenties.