The question for the rider is what is the rider's intention with the use of the half halt, and what is their TIMING.  

A hh only 'works' or 'goes through' if the horse is first in a balance where the hindlegs are already in a balance, and the rider is making little differences.  And then the question is what kind of hh?  Bilateral: seat/lleg into both hands? Diagonal: inside leg to outside rein to straighten/control the shoulders/etc? Or lateral (inside leg/hand to move horse over or outside leg/hand to receive or perhaps slow the tempo or rebalance?)

If the horse is going through a hh then likely it is too slow/too rounded/too quick or too on the forehand to 'fold the hindlegs' more effectually and respond.

If the horse is clenching the jaw, then a change of balance first is in order. And perhaps a totally different relationship with the (use of the) bit with in hand work first to mobilize the jaw/change balance before the rider mounts.  Imho that is the time for an arret or demi arret to get the horse more up or open. Sometimes a step of leg yield can change the horse's balance in the first place.

Next is the use of hh, which ideally should be learned by the horse ask 'alert/alert/do'. In that way the horse is not ambushed.  A rider can think diagonal aids of en/large (two seperate messages, and then re/balance (or slow/down depending upon the need).  It is usually leg before hand as well.  Otherwise the horse merely falls against the hand (driving with the handbrake on).  

The rider sets the horse up for success.  The rider must ask for the slow/down BEFORE the tempo increases.  It is the rider's job act first and to solicit reaction (ie same tempo) rather than constantly be the victum of the horse (repair the damage).

So, what would I do?  Tell the rider the TIMING of the aids, and the TYPE of hh desired and WHY.  Then have them 'play' with the possibilities.

It is difficult not being able to see the horse and rider in person to give advice, but from your description I would surmise the following -

First -- Remember that when the horse fails to do what we wish, it is a communication error - ON THE PART OF THE RIDER, always on the part of the rider.

When you mention that the horse barrels through the half halts immediately I knew you would follow up with a remark that she is bracing in the jaw and showing resistance there. Before the half halt can be effective the resistance in the jaw has to be remedied. If you follow anything on Classical Masters there are several who remark on this starting with Baucher through Beudant, L'Hotte, Faverot de Kerbrech, etc.

My initial guess is this however - the rider's hands are contributing to the horse's bracing against the bit and the action of the half halt, this is the case the majority of the time. Behind the hands is the seat so really from the ground up I would look at how the horse/rider team is put together. If the rider's seat is at fault in any way that will be magnified through to the reins and eventually show up as resistance in the horse.

Another tell-tale that the rider's seat is out of sorts is that the horse is overly sensitive to the legs. When the legs are not able to work independently, are positioned in a way that does not assist but instead provokes the horse, are inconsistent in their contact and give cues that are unintentional it is enough to make a horse react in this way. The reason is because the horse learns over time that they cannot trust what the rider's true intention of leg cues is - whether the leg touching his side means to go faster or if it is simply the rider unintentionally touching his sides. Get the idea?

Once the seat of the rider is sorted out the leg issue should go away on its own - literally. If the seat remains out of sorts the leg issue will remain.

Coming back to the hands and the half halt. Baucher stressed the importance of flexions, but without going to that extreme there are things you can do to assist in relaxing the horse's tension once the rider's seat and hands are improved, steady and light (and I stress the point of lightness on the rider's part - the horse can only pull against the pull of the rider's hands...). The full halts will help if the horse is resisting with their weight - by that I mean going on the forehand, 'pulling' by simply bearing down the weight of their own head. If the horse is resisting with force - by engaging their muscles - then the full halt will do nothing to remedy this. Vibrations on the reins however will. These are done lightly and by moving the hand side to side as though the wrist is a door hinge - rather than pulling the reins forwards and back. Can be done on a single rein or both at the same time - though a single rein is preferred as it is best in these cases to go back to working on a single rein anyhow to simplify the cues the horse has to interpret.

Vibrate, once the resistance ceases for even a millisecond stop the action and return to normal. When the resistance starts again use the vibration again. Vibration is akin to massage - if you've ever held onto something that vibrates for very long you'll find that your grip becomes weaker and weaker the longer you hold on, same principle.

Sounds like she might be used by several riders too? Lesson horse, or previously used for lessons? These horses tend to learn to cope with a variety of riders at rough stages in their seat and cueing ability so would not be surprising.

My gelding, formerly trained as a jumper and purchased at the Elite hanoverian auction, had no brakes either at first. My trainer and I surmised that he'd been ridden by tall, strong German men and he either couldn't "hear"short little me or had never learned a subtle half-halt. Perhaps due to his back injury he'd just learned to "run away" from discomfort. We may never know.

We fixed it by riding him into fences and walls while applying half-halt aids. He figured it out pretty quickly.

Maybe not the fix for every horse, and it started out a little bit Western, but it worked for us.