If she's doing this on the ground it needs to be addressed there, first. Will she lead with slack in the rope? When you ask her to stop, does stop off your body language before she hits the end of the slack, after feeling slack come out of the rope, or does it take her a few steps of pressure on her nose (all slack out of the lead rope) to drag to a halt? Does she back up softly on the ground or do you have to push her back? When she does back, is she taking large, deliberate straight steps backwards or does she drag her feet in the dirt taking little steps more to the side? Will she turn on her haunches when you purposefully walk into her forehand? Will she stand tied quietly by herself for at least a moderate period of time?
I have a strong suspicion that this horse needs a ton more groundwork. You likely won't be able to achieve responsiveness and softness in the saddle if this horse has no idea how to be soft and maintain float in the rope on the ground. I also would suggest getting under saddle basics down in a ring or enclosed area before taking her out on the road - at the very least she needs to move forward willingly with light pressure, soft and able to bend to both sides, stop and back up softly. I 200% agree that you need to see a good trainer. I don't think you have the knowledge or experience to do this alone.