Let's put it this way, I never ride my horses in a rope halter. What may be happening is that halter is rotating and pulling sensitive hairs away from her eyes. I've seen it happen a lot with rope halters. A four year old isn't going to be ridden by children anytime soon. So get her in a snaffle bit and get her trained right, get her understanding collection, use a lot of leg and never let her get her head away from you, but dont haul on her mouth either. After she is finished right, she will ride in anything. In my experience, Most horses that are trained correctly will ride in whatever you have handy..
~Started young horses in Bosca te Ador, unto the two rein the old Spanish spade, brought them along with two hands that were gentle. Some fine reining horses as ever were made~