Your problem with this mare has absolutely nothing to do with some magical 'bond' or the fact that you are there where she can see you. I have 'coached' owners wanting to train their own horses that have had the exact same problem.
I wrote an article several years ago for the 'Quarter Horse Journal' titled "Trading Aids". It explained how you start out teaching a certain maneuver or action with one 'aid' (or several aids) and gradually transfer that request to a much more mild and 'imperceptible' aid that is more pleasant to the horse.
'Trading Aids' is what every trainer does, but they usually do not consciously think about it. It is what you need to do. Since this has not come naturally to you, you need a plan.
When ground driving or making a horse move forward, I usually 'smooch' at the same time that I give a horse a physical reason to move forward. I will smooch at the same time I slap the reins high up on the horse's rump. I don't just drive one around a round pen or the arena, I drive one up and down hills, across ditches, over fallen trees, across a concrete driveway and on and on. You get the point. I want the horse to learn that a 'smooch' means to move forward wherever I point its head. If the smooch does not create the necessary forward impulsion by itself, then it is followed by whatever it takes to get the impulsion needed. Very quickly, the horse will learn to move from just the smooch.
Then, the rider does the same thing on the horse's back. Smooch first followed by a slap of the reins on the horse's butt and a simultaneous 'squeeze' (not kick) of the rider's legs. Up until now, pressure on the horse's ribs has not meant 'move forward'. It is your job to gradually 'trade' the slap and the smooch over to a light 'leg aid'.
So, her rider (with you there or not) needs to create the necessary forward impulsion needed to move her forward. The most effective thing you can do is additional ground driving in a more meaningful way by driving her places she does not just automatically go. You need to drive her and then ride her (or have her ridden) while giving her a good enough reason to go forward.