REtraining? Was she previously ridden Western Pleasure? And had years of work where the rider kind of snaps the rein up in order to "set her head"? The horse MUST keep their head down or they get snapped in the mouth, they put their head down and get rewarded with looping rein with no contact more than the weight of the reins. Horse becomes worried about contact, since it's a BAD thing, in that kind of training.
So, your horse is probably a lot worried about contact, is braced in her neck and poll and jaw, and when you start to post, she gets even more worried. It can also be that the saddle you ride in is not very comfortable and she tightens up her back, dropping it down, too.
I bet that this tightness and worry about contact is evident at the walk, too, but you just aren't noticing. She might not barge the reins, but she is likely not soft on contact at the walk, either.
I would work at the walk, teaching her to accept contact. That is what your next thread might be on, but I don't have time to write that out now.