There are a lot of variables when it comes to why your horse doesn’t turn too well, and I wouldn’t quite settle on the bit being the main reason. However, it could definitely be one piece of the puzzle. I know from experience, generally it’s easier to engage and help a horse turn in something like a snaffle vs a kimberwhick. If I were you I would try a full cheek.
Myler bit is amazing but they are expensive. They are great for your horse because they are only as strong as the rider makes it. Meaning if you don’t want to engage the bit you don’t have to make it less painful for your horse
Without sounding judgemental or as if I know it all but from experience, you can change the equipment/bit as often as you like but it's not going to fix your problem either at all or long term. This issue needs training, time & patience. Start from the ground & work your way up, build up the relationship between you & your horse, get the cues understood & trained. In the meantime, it may be worth having your horse health checked teeth etc & a tack fitter to check your saddle etc as something so simple can cause such a multitude of problems. Good Luck :)
Waterford full cheek is good for a very strong mare I had, I’d also work on the horses schooling and get them to steer off leg and work on lateral movements such as the leg yield which will help steering and work on the horse listening to your seat and voice for stopping/slowing down