When I lease out my horse or have someone less experienced ride her, she always goes in a french-mouth loose ring.
Back when I rode her consistently or she was jumping I rode her in a corkscrew dee ring because it's what I felt she went best in.
However I wasn't comfortable with less experienced hands and that bit - and I don't think it's necessary for someone just hacking or trotting cross rails.
If it were me I'd probably switch the horse to something milder. If he's quiet and doesn't need extra brakes I bet he'd be happier in something that he can't accidentally be punished (as much ;)) in.
So what's the absolutely mildest bit there is? My mom loves him to death and obviously wouldn't ever jerk on his face on purpose, but she is learning and isn't very balanced, and my main concern about her riding him was the fact that she could potentially hit him in the mouth.
I'd say a loose ring. You can always think about adding a neck strap, that would give her something to grab if she does loose her balance.
Completely outside my realm of expertise here, so take this with a grain of salt.
What about a hackamore with the chinstrap on really loose? If she happens to pull, he'll get a little bonk on the nose, but that should probably be the worst of it, right?
Color me confused.
Your horse is a saint, but you ride him in a twisted snaffle, pizza cutter spurs, and carry a dressage whip.
I would just switch him to a eggbut with a french-link. Thick can be nicer, until you reach a point where it's uncomfortable for him. The trainer should keep her from bonking him too hard. And hackamores aren't more gentle.
Since you have him in a full cheek...I'd would use a full cheek or D-ring double jointed snaffle. If he likes thin bits, you don't need to go too fat. And add a neck strap for you mom. Her hands should be in it at all times for a while.
My coming-back-down-the-ranks mare sounds a bit similar.....well, you don't say whether he's the "dead" type or not, but my mare is. She can lug and lean like no other, but she will pack around the kid and adult I let ride her like no other :) I have 3 bits of choice for that scenario (beginner-type rider):
1. For a rider with decent balance I have her go in her D-ring, low port Myler (MB43LP). This keeps her nicely balanced but doesn't bother her if the rider bumps her a little bit here or there. (this is actually the bit I showed her in for 90% of her show career, just with a curb chain added at shows).
2. For a rider with "okay" balance, but more prone to balancing off of hands, I'll use my french link D-ring.
3. When I put my 4yo daughter up, I use my 2-ring happy mouth gag bit with a rein only on the snaffle ring. So essentially a loose ring, french link, happy mouth bit. She can bounce around all she wants without bothering my mare, but it would be a poor choice for a rider really wanting to "ride."
I would not use a hackamore as a substitute. I think hackamores are great and have their place, but they carry a fair amount of leverage and I would rather have a rider bump the horse with a soft snaffle bit than in a hackamore. If you wanted to go the bitless route and your horse was well behaved enough for it, I might try a side pull.
You could try a rubber mullen mouth D ring or loose ring. It doesn't get much more mild than that.
Would he go in a 'jumping hackamore'? My old mare loves hers. It's a thick rolled leather noseband that the reins attach to making the bridle a sidepull. It's basically like riding in a halter. She played polo in a gag with draw reins, but will calmly pack a kid around a hunter course bitless.
It's basically impossible to hurt her with that. And she's one to toss people in protest if something is uncomfortable/unfair. She was at a different barn and started rearing and flinging people. Turned out they were putting her in a series of increasingly harsh bits for uneducated hands. I'd throw people too. Moved her, put her in the jumping hackamore and she went back to being the packer saint and quickly became the barn favorite.