Have you tried riding without reins? Stash them safely and use a neck rope to ride without. That will fix both problems as you can use your hands to turn nor see saw him in the mouth.
But just be careful. You have to be an active rider. Actively thinking "What am I asking, what am I doing.. what should my hands/legs/seat/eyes be doing?
Your seat guides the direction, your legs encourage the horse (or ask the horse to yield to them), and your hands come in last. You'll figure it out
"Strength is the ability to use a muscle without tension"