Looks like I lost my bet on the Green part....ha! Well, that's good news! This horse does know things and is well trained. Great.
She was used as a cutting horse for many years. She is 12 yrs old. She has also been used as a broodmare and has not been consistently ridden for about two years. She is being boarded at the place where we purchased her. The previous owner only rode her once and said she didn't have any problems. I have only had her for a week.
Ah ha! Okay, if you can rule out any pain issues (pinching saddle, teeth, painful cycle, etc)
Then, how are your riding skills?
I had a client horse do the exact same thing...she would just stand there when the client would climb aboard...the problem? The client was just SITTING in the saddle.
There was no energy from the rider. She didn't know how to use her seat/her body to tell the horse to bring up her energy for moving out.
Sit up straight with a line from your shoulder, your hip and your heel. Be sure to have your heels down slightly and your toes pointed forwardish....relax your body.... ROLL your hips (squeeze your butt cheeks and release, over and over again).....then send that energy down to your calves and squeeze as you roll your hips and then "kiss" and spank (over under motion with the lead part of a macate rein).....or a crop (tap...1...2...3...4...getting louder with each tap)
Soon as the horse moves forward, release all pressure but keep your hips moving slightly with the rhtyhm to keep the horse going...it's a signal to the horse that you wish to keep riding.
Soon as you stop rolling the hips and squeeze and hold for a stop, the horse learns to stop.
Add more squeeze and such for a trot and more for a lope...
Once my client learned to use her hips and move with the horse and not simply SIT in the saddle....the horse moved off and she was walking, trotting and loping without any trouble every time she asked.
That was it....it was her lack of use of her seat. Might be your problem, too.