I don't think we need to "dominate" our horses to get their trust, but we do need to be predictable when you handle them, in that they need to know that every time we give them a cue to do something, provided they respond with the correct response we immediately remove the pressure of the cue. We all largely train horses with negative reinforcement, so often the pressures we use to motivate them to do what we want are unpleasant for them, and often those cues elicit the unwanted flight and anxiety responses which put us and them in danger, or make handling them a hassle.
Calmness, relaxation and softness in interactions with humans arises out of the horse being able to predict the outcome of an unpleasant cue and control how much of the cue they are exposed to (by choosing how long they will put up with it until the do something to make it go away).
As we get better at knowing just how much (ideally how little) pressure to apply to get the correct response and most importantly know when to release it to reward that correct response we give the horse predicability and control. The horse doesn't have to second guess, doesn't have to be on edge expecting a strong or frightening cue coming out of nowhere.
What also accelerates calmness is that every time you apply a cue, the horse always gives the response you want and that you don't release the effect of the cue until it does. This increases the predictability- if sometimes when you lead her she walks straight beside you but sometimes she wobbles into your space and you shake the leadrope at her and give her a fright her interaction with you isn't predictable so she has to second guess. Much better to correct the wobbles each time so she learns that she should walk straight next to you each time- makes her calm and you feel safe.
Its not about dominance or respect-rather think of all your interactions as being whether the horse responds to your cues as you want or not. Horses are not pre-programmed to like and want to spend time with horses, we actually have to specifically train them to do this (spend time with at least) so when things go wrong, we need to consider what has gone wrong with their training (and their health for many issues).
On those times she doesn't respond correctly to a cue consider, what action of yours (or the evironment or her past learning) might have either motivated her to respond incorrectly, or rewarded the incorrrect response.
You then have the tools to correct what you do, so you can correct the horse, which leads to error free training and the payoff should be a calm, "trusting" happy to hang out with you horse. Her world is predicatable and controllable and interacting with you becomes something that is associated with a calm, relaxed frame of mind. Good ground work execises like those of Clinton Anderson are excellent because they meet the control and predicability critera and by training the human to be really clear in applying the cue and its release, make things much easier for the horse.
We use this way of analysing how our horses interact with us with all our horses and find they all end up the same, given temperament differences. Some horses are always more likely to trial escape/flight responses than others and some need more reptitions of lessons before they clearly understand how to control how much of the pressure they are exposed to and how to make their lives predictable in their dealings with us. Obviously this relies on us as handlers giving them every chance to respond to light cues so they don't have to experience the heavy ones. If we always use heavy cues the horse never gets the chance to respond to light ones and that can make them nervous because the strong cue comes out of nowhere or they form an association between being ridden and handled and being exposed to frequent unpleasant pressures they can't avoid.
In research in dogs and rats, scientists found that the animals given the chance to predict when an electric shock was going to be applied or who learned how to avoid it by doing a trained task were much less stressed both physiologically (cortisol levels) and behaviourally, than animals exposed to random shocks they couldn't predict or avoid.
Good luck with your mare.