Hi, I realise some of my reply is rather terse, as you sound like you don't get what's happening or the potential of it. I also appreciate I may have perceived the situation from your words incorrectly. So respectfully...
If you care about your horse and she is suffering from your current management, change it!! Yes, might mean you have to move her, pay more, do things differently, but if you won't change it, don't expect anything to get better - it'll only likely get worse for her! It is common enough for horses to suffer because owners are unaware of problems, but to continue doing something that you know is causing your horse to suffer is classed as cruelty IMO & is not acceptable.
If your horse is only let out in a grazing muzzle at night & locked up every day, then I assume she already has known problems - is IR, laminitic, obese or such?? So she's already extra sensitive & already needs careful management if you don't want to let her founder & other probs.
'Awful diarrhea' is likely due to acidosis - caused by starch overload to the hind gut. Probably more about quality than quantity of the grass. Esp if she's extra sensitive, avoiding 'cattle fattening, improved pastures', such as rye grass, clover, fertilised, etc is important. Depends, but generally speaking, native grasses are much lower sugars & more 'horse friendly'.
It could be the opposite - tummy ache & ulcers due to going hungry, not able to eat enough thru the muzzle, as someone suggested, but having had horses with muzzles on all kinds of grass, yes, they can find it a bit harder with long stuff, & some horses don't cope with muzzles, but it's not a likely problem that they go hungry.
That she is uncomfortable under saddle & unwilling to trot could be ulcers/gut pain, &/or laminitis(altho kicking out sounds more like gut pain.
If she's locked in a stall every day, all day, I'd absolutely want to change that, get her out & able to be a horse. For her health as well as wellbeing. If you absolutely must keep her locked up so much, best to have her in a large yard with another horse for company at least. And you'll need to provide lots of exercise, as she will be getting very little(horses, esp if locked up all day, don't do a lot of walking around at night).
Free choice hay may also be too much for her, but it's not good to let a horse go hungry for long periods, so a small holed hay net can be an effective answer for that. If hay is particularly rich(eg cut from 'improved' fields), it may also be too much for her, so may need to be soaked & drained first, to leach out some sugars. Grass only loses sugars in active growing, so hay can be just as rich as the grass it was cut from.
Nutritional balance is also a likely problem, which can make problems such as body & hoof pain more likely. Ensuring she's getting *appropriate* nutritional supplements, to 'fill the holes' in her particular diet is also important.