That's great that she's enjoying her job! You must be doing something right if that's the case.
When you say "roller," do you mean a surcingle with lots of rings, the driving saddle itself, or something else? I just want to make sure we're talking about the same piece of equipment before I give you any advice. I think generally speaking running the makeshift check rein to the halter is a lovely idea. It gives you the same preventative action without interferring with the bit in any way or causing her to yank her mouth. Wonderful!
You may find only running it to the back of the halter doesn't actually prevent her from eating so be prepared to run it down to the halter rings like a regular side check.
Regarding direct rein vs indirect rein, you'll find that the answer or at least my version of it is a bit confusing. Since driving reins are always supposed to be run through some level of terret ring to keep them from dangling dangerously there really is never a direct rein in the sense that you are using it. I can see where for the first few lessons in a halter you might be doing that but I'd wean the horse off it as soon as possible by gradually bringing your hand back into the standard position until you aren't moving them sideways at all to signal a turn. The terrets supposedly keep the horse from feeling any directional reining so unlike a riding horse just about everything will be done via half-halts and balancing the pressure between one rein and the other. Now what's confusing is that right after your trainer and all the driving books out there get done telling you that, they then insist that you must still keep your hands in a straight line to the bit just as in riding and that you must keep your shoulders straight and your hands together because if you move them the horse will follow your rein!
And what's worse, they're right!
OH! LOL. So they both can and can't feel directional movements of the reins when driving. Basically what is correct is to move your elbow straight back to tighten the rein, preferrably without dropping your hand. Don't move it to the outside and don't suck it inwards towards your opposite hand and chest to take up rein like I always catch myself doing.
The correct way as I've been taught it to go through a turn is this:
-Think deep and think ahead. When you are walking towards a corner in an arena, think like you are going to walk forward beyond that arena wall until you are actually ready to begin your turn. Keep your eyes up and focused ahead. Breathe deeply and relaxedly. If you start anticipating the turn, so will your horse. I've found driving and riding are both very zen-like-- when you're trotting a straight line, you're on the straight line until you're not!
Don't get ahead of yourself.
-When it is time to begin the turn keep your shoulders up and back, your body erect, and your abdominal muscles taut (pretend there is a string attached to the top of your head pulling you up). Give the horse a gentle half-halt on the outside rein to let her know something is coming and then turn your eyes and upper body in the direction you wish to go; imagine that your belly button is a flashlight and shine the light along your path. Breath!
-Your outside rein holds the horse out on the circle or path, the inside rein asks for the bend. Rather than pulling your horse into the turn with the inside rein as you would when riding you half-halt on the inside to get them to soften the jaw and bend and then as the bend is produced you feed the outside rein just enough to allow the turn. Usually turning your upper body in the manner described above will give you enough give in the outside rein but you may have to move that hand forward slightly more to follow the horse. As you complete the turn you gently take up the outside rein again (moving your hand and arm back, not shortening the rein in your hand) which has the effect of "disallowing" further turning. Think of it like steering a bicyle- you can't pull back on one handlebar without moving the other one forward. When you pull the outside "handlebar" back again you'll have to give with the inside one too, otherwise you bottle the horse up and they will break gait or stop in confusion.
-You should now be back on a straight line. Continue your relaxed deep breaths and drive to the next corner!
Now having given you all that detail let me clarify that what I've described is a proper turn as done in driven dressage. That's about as complicated as it gets!
The breed show ring has different standards and I believe from what friends have told me that they do use a sort of "opening hand" on the inside to invite the horse to step through it and over in order to turn. And of course when you're ground-driving in a halter or simply out on the trail pulling on one rein or the other works just fine. But I wanted to share the most complicated way of doing it because the tools that you use in such a turn are the foundation of everything else and may be helpful in correcting other problems as you go along. For now just remember that when trail driving you can either use a check to support the horse and the reins only signal left, right, or whoa, or if you don't have a check you MUST hold contact at all times so the horse knows they're not alone out there. Contact should be friendly, not something the horse resents. Then making turns and changing speeds is a matter of how much pressure you take up or release and that's where the type of turn I describe above comes in.
Draft-style or farm/Amish-style driving is very different because their entire set of goals, priorities, and horse-handling are different. Each one works and you've just got to pick the direction you want to go in. The style I use is called "carriage driving" and is different from "show driving" although I do compete. Don't stress too much over any of this as A) horses are very forgiving, B) she can always learn a different way to do things later, and C) right now all she's really learning is how to give to pressure. Anything more complicated than "left means left and right means right" can come later!
Hope I haven't completely overwhelmed you. Drive on!
Leia
Edited for the one typo I missed