@centaursam,
There are two main uses of homework rides, to practice what you learned in the lesson or to train the horse.
This 5 year old mare does not sound to me that she has ever had anything clearly explained to her in a way she truly understands. Perhaps the trainer did not release the aids in time, maybe the trainer was following an outside schedule not allowing those long, slow hours until the horse calmly UNDERSTANDS what the rider is asking for. Since you are not getting satisfactory results riding her I recommend devoting your homework rides to training her from the very beginning of mounted work as if she were a weak three year old who needs to develop MUSCLES and endurance before she can profitably move on to anything else.
She is telling you that you are somehow blocking her movement. At the walk I suspect that for some reason your seatbones are blocking her big back muscles, the ones that give the feel that the horse’s back is “swinging” when they alternate. The muscle thrusts your seatbone up as the hind leg on that side pushes off. Your seatbone also moves forward a little bit while at the same time it moves up.
If I was paying to ride this mare in a homework ride I would start with several months of just walking. Walk with sagging reins at first (loose reins “holding the buckle” swing and often irritate the horse’s mouth) just walk, at her speed at first, concentrating on following every movement of her back muscles LIGHTLY (do not bear down with your seatbone, concentrate on moving your seatbone going UP.)
This is not a quick and easy solution. I have spent months of my homework rides just walking the horse. I concentrate on keeping my seat light by following the movement of the back muscles, I move my hands like I keep contact even though my reins are sagging and I do NOT really have any contact. I keep breathing. All my aids are well timed (much easier at the walk for you) and I release them immediately.
As the mare gets stronger you can add stuff, working on turns–first gradual turns, working at getting three speed of the walk (transitions!), and working gradually on turns in place.
If this mare does not have medical reasons for her actions I can pretty well guarantee you that after several months of these once a week homework rides this mare will look forward to you riding her, she will understand what you are saying to her, she may start to take an interest in doing her work well, and she could even ENJOY you riding her.
When you get to this point everything else is easy so long as you do not block the horse’s movement all the time or hurt the horse.
Start at the beginning of mounted work. Spend time at this. In the long run you will be very pleased with your results.