You said she charged you with it when you longed her with it. Your words, not mine.
The problem with that is that right there she is either demonstrating fear or a lack of respect. One or the other. And that will carry over into the saddle.
most likely the poor horse was abused in the past, and you appear to be advocating this person proceed with more abuse of the horse in order to make the horse “respect” him/her.
Beating up a horse doesn’t make the horse respect you. If your dad or a bully beats you or forces you to something do you “respect” him? no, you learn to hate him, distrust him and you just might try to attack him sometime. That’s what this horse is doing with the lunge whip. Most horses don’t mind lunge whips because they are just directional tools but perhaps someone actually whipped the horse with one in the past. If the horse lunges just fine off voice, then why bring the whip into it?
Clever trainers don’t push animals to the point where they feel they have to explode and fight back. With an animal as big as a horse provoking a fight is a really bad idea. Any hack trainers who go around spouting off silly words like “respect”, by which they usually mean “beat and bully the animal until it shuts down” are the kind of people who end up causing train-wrecks.
Training is best done slowly and gently in baby steps, with the animal set up to succeed and enjoy each step. Reinforcement, both positive and negative, is used to alter the animal’s behavior and teach the animal what behaviors are wanted. Respect is completely irrelevant. I’m not even sure animals understand the concept.
The real, and only, issue here is the horse won’t move when mounted. Rule out some kind of pain issue first obviously. The safest thing to do is to get someone to just lead the horse with the rider up- and try to make it fun for the horse. Work the horse on the ground, then get on the horse, then have someone lead the mounted horse a few feet and reward by feeding a treat. Gradually extend the length of the rides. Next move on to having the mounted horse follow a group of other mounted horses for a short distance. Gradual, gentle baby steps. Make sure to not even try to provoke the horse into a reaction- get off and walk away if necessary. Maybe move on to gentle, relaxed trail rides following other horses- most horses enjoy going on trail rides. Alternatively, you can try “waiting her out.” Most horses won’t stand motionless for hours, especially if you cleverly mount her out in the blazing sun. EVENTUALLY she’ll move a few feet and then you can praise and reward and get off and put her up. So she learns it’s easier to just move than stand there motionless.
The OP talks about building trust- one of the easiest ways to build trust is clicker-train ground work with a horse. You can train horses into the most wonderful ground manners with a clicker, without ever having to the make the horse “respect” you, and a side-effect is the horse a) learns to trust people, making it less likely the horse will hurt anyone, and b) learns to follow along and tolerate the weird things people do without complaint, again making it much less likely the horse will hurt anyone.