I feel like with the regular snaffle he does not respond to my half halts or my pressure on the reins. I don't jerk him in the mouth or anything, but when I have contact and give him the q\cues to lower his poll and go on the bit he completely ignored them, he runs around with his head up and avoids it no matter what I do and how much I increase the intensity of the cues. I have very quiet hands, so I don't think he's hard mouthed, just simply not paying attention to my cues. He only listens to my cues when I'm asking him to lower a gait or stop.
When he was ridden in the hanging snaffle he paid much more attention to my signals and kept his head down nicely and paid attention to my half halts and cues. I feel like he rode much better with the hanging snaffle, but the only problem is he would get very fresh if your hands weren't quiet. My mom has somewhat unsteady hands so we switched to the snaffle for her benefit, I however have my own bridle now and am considering switching my bit back to the hanging snaffle. Do I have good ground to do this? Is this a situation where it is appropriate to switch my bit to a slightly stronger one?