Turning the horse wrong?

[SavvySAM]

Not in English you're not. Never cross the rein over the withers. However you SHOULD bring the opposite rein closer to the neck, and put pressure/leg (NOT kick) on the same side as the direction you're turning. (However, at lower levels, you may use leg on the outside no problem.) So if you're turning right, bring the left rein into the left side of the neck while giving just ever so slightly, and hold the right rein. You may pull the right rein ever so slightly by squeezing your bottom fingers on the rein. Subtlety is golden! Then at the same time, turn your hips just a tiny bit in the saddle in the direction you're turning while bending the horse AROUND your inside leg. Instead of the horse just moving away from your leg, they learn to bend around it and have a nice bend on the circle/curve/pass. There are a combination of leg cues you can adapt.
Using reins directly as you say you do, can easily make your horse hollow and not have a good bend in the neck. It can be used, but it's preferable to give the outside rein and hold the inside when turning. Look up Manolo Mendez dressage. SUPURB horseman, and a true advocate for the horse. He knows his stuff. And even if you don't do dressage, it applies to all things riding. I'll give you the link to his facebook page. So excellent. https://www.facebook.com/ManoloMendezDressage?fref=ts