I have a 10 year old Kiger Mustang mare (Trillium - or Trill) who I have had since she was about a year old. We have been through the thick and thin of training together and all usually goes fairly well, but I have recently discovered an embarrassing gap in her development: she has a sloppy halt and even sloppier down transitions.
She has always tended to wander out of an (initially) nice square halt in exciting or distracting situations (i.e. At a show), so I know this issue has been hiding in the background for a while - but since we have started to work on more difficult transitions (trot to halt, canter to walk, etc.) the problem has reared its ugly head in a big way.
I also have a beginner taking lessons on her occasionally and Trill is very patient EXCEPT when it comes to down transitions, which she completely runs through. This is getting frustrating for my young rider, especially since she has not developed her seat enough to firmly ask again when the horse ignores her. Ultimately working on this issue will improve her riding but there is no need, at this point, to push her beyond her skill level on a horse that is not a schoolmaster.
Anyhow, conformationally Trill is a bit on the forehand and tends to be lazy about crisp transitions. We have worked through this problem as far as upward transitions go, but when it comes to the downward transitions, especially when skipping a gait, she falls in at the shoulder and comes down hard on the forehand, leading her to come off balance and rush through the transition.
I have been working on my own position fairly diligently to make sure I am not negatively influencing her body position, and have made improvements as far as that goes.
I also recently switched to a jointed kimberwick from a loose ring snaffle for training purposes. Please note that I would be the first to discourage another rider from graduating to a more severe bit in order to improve performance (I think every horse is capable of working in a fat snaffle), but the chain and extra leverage is proving handy as a last resort backup to my seat and leg aids, and I have already begun to get an improvement through using this new bit. When we are just hacking out or jumping I have been switching back to her old snaffle with decent results. I don't want to be stuck in a kimberwick! (especially since they're illegal in the dressage ring)
Anyhow, a typical ride includes a nice long warmup on a loose reign, followed by lots of circles and changes of bend working her on the bit (which she does fairly correctly if warmed up well) at all three gaits, then lateral work with LOTS of transitions built in there. I can get her working through from behind without too much trouble, but it all falls apart when I ask for a crisp down transition. Head goes up, mouth gets hard, and she powers through the aids. This is ultimately why I switched to the kimberwick, as I can give a quick strong aid and release immediately rather than feeling like I am getting into a pulling match.
We've been working on reinforcing the verbal "WOAH" aid on the ground too.
I feel like our problem is a combination between Trill ignoring the aids and having poor balance in that split second between moving forward and stopping or slowing from behind.
Clearly, an ideal situation would be to find a trainer to give us lessons (it's been WAY too long
Thanks in advance! Here's a few pictures of us riding for reference: (all taken about a month or two ago in the snaffle bit)

Backing

Nice trot

A bit stiff

Better

Overbent shoulder-in

Walk