I'm not going to say it is wrong as people have different ways of teaching like you said. But it also depends on what kind of turn around you want. A reining horse, cow horse dry work turn around/spin or a cutting horse turn. There are slight differences between the reining and RCH dry work but the big fundamental difference is between the cutting horse turn on a cow and a reining pattern spin. Many say the most difficult thing to teach a reined cow horse is both because of that difference. Or teaching a horse who was originally a cutter to spin because of that draw.
The cutting horse pivots on the outside hind and uses that draw your mares have. The front end backs around the hind end. The turnaround spin is a forward movement, pivoting on the inside hind. A really small circle where the front end moves faster than the hind.
I ride with a trainer who has a very weird way of training the turnaround/ spin, but it works for him and the trainer he rode under. He uses no inside leg to move the rib. I probably use my inside leg more than anything, especially when initiating the spin to create bend, get the rib out of the way so the shoulder hence front inside foot can back for the outside front to sweep across for the step over. Learninf to ride the filly I sent him has been tough. Either turn for the cutter or reiner I get the rib out of the way. (However you can get them overbent causing them to fall on the front end and the outside hip flips out). It really is a balancing act!
I think you're on the right track! You'll be able to use that draw to your advantage just as long as she doesn't dive into it and if she only makes one or two correct steps in that turn you can choose to just stop and pet on her or ride her out. If you let her walk down into the turnaround/spin and she gets hung up and is swapping ends drive you can drive her back out to the small correct trot circle to show her where you want her, when she gives you can it let her walk down into it again.
My advice is find what motivates her. It is so frustrating to ride a ride a horse that is talented but feels like a puke doing dry work trying to make them handier for the fun stuff! Horses that need something like an old cow or even tracking the dogs(be careful that doesn't become a habit but I've used it) or barn cats?
Hooey was horrible at dry work but come to life if he had something to work. That horse, rather than leaning towards the gate to the saddle barn would lean or try to stop at the gate to let the cattle in the arena. And no joke, my Chihuahua helped teach him how to spin after I don't know how long of me trying to teach it. (The hackamore helped a bunch too, he didn't like the snaffle)
He would torture dogs or cats, the Chihuahua was always in the arena and Hooey would seek him out to paw him into the ground, Chihuahua would always dart to the side and slightly back and it put Hooey in a good position to turn. I killed two birds with one stone, all of a sudden Hooey understood the turnaround and the Chihuahua stayed out of the arena..LOL
Very frustrating. She has a lot of jam when it comes to working cows, roping, and riding out but the moment I ask for a little dry work I have to really work for everything. Even sorting on gravel and mud the other day she was way lighter and more sat back on her hocks than I could probably every convince her to be without cow critters.
We have a bunch of yearlings, and three big goofy highland steers that would be fun to work. The only problem right now is that it's still icy in a lot of places where it would be nice to hold critters up to work them. I need to be better friends with someone who has an arena and a mechanical cow!!