Does she react that way when she is tied for everything you do with her?
I think you can teach her to feel safe being tied if you start from scratch as if she is a filly just learning everything brand new. It sounds like she equates being tied with something negative, so she needs to be literally re-programmed to learn that it's ok. She has to trust you and know that you will help her relearn and not allow her to be harmed when tied. It may take months or years but if you begin from scratch and make the experience entirely positive, enjoyable and rewarding, she stands a chance of getting over it.
I would start by always having a second person hold her lead if possible when grooming, saddling, trimming, etc. If that isn't possible for whatever you're doing with her, then hold the lead yourself in your hand and make sure nothing you do when working with her involves her being tied.
Then, when you have your tying lessons, that is a completely separate and very reward experience which has nothing to do with anything else. Simply don't tie the rope but wrap it (not high up and give a good 2 feet of rope). Use a soft nylon halter, not a rope halter, and cotton lead rope. Keeping the rope wrapped around once but not tied so she can always choose to pull back, stay next to her and keep your hand on the lead rope and give her a treat and praise her for standing. If you can make this a daily lesson, just hang out and do this for a few minutes at first, then undo the rope and walk her around for a minute, lead her back to the area to "tie" and give her a treat and gobs of dramatic praise, then make your tying lessons a little longer each time. Stay next to her and to the rope. When she is calm and you think you can take a step back and she won't panic, take one step back. Baby steps. Eventually she'll equate the experience in her mind with a very positive and enjoyable experience. If you think of your 19 year old mare as a small filly inside that big body who needs your comfort and security with these lessons, that may help.
As she grows more comfortable and looks forward to her tying experience, in time I'm sure you can start incorporating it into more routine work - if she pulls back for any reason after she has learned to be comfortable and trust, I would respect whatever her reasons are and find out what is happening and look for a better solution.
Just some ideas which I hope are helpful.