Don’t you just hate people sometimes? My mare was also abused – can’t touch her ears, flips out if she sees a jump and is terrified of whips. Have you thought of working her in long lines? My gelding (OT Arabian) will take off like shot from a cannon if one uses heels, and needs very, very little leg, so I taught him all the words for whatever I want him to do (makes me look good, too), including figure 8, serpentine, circle, spiral, reverse, diagonal line, half pass, etc., as well as the usual WTC, halt and back, all in long lines. I wouldn’t say “make your horse love you”, but she does have to trust and respect you, and that can take a lot of time. As for yourself, you need to trust her (hard to do if she is dumping you), and relax. I found St. John’s Wort helped me with relaxing after a bad fall last summer (long story). Also, I find that I am more relaxed if I do not use a saddle, and rely on balance. Some days, all I do is hop on and walk around in the patterns, then hop off. Not only does it relax them, they don’t know what to expect, so they are less likely to anticipate and leave me in the dust somewhere. If she does start to take off, make her turn in small circles – she will stop rather than fall herself. I don’t have much experience with Quarter Horses, only Thoroughbreds and Arabians, so I can’t even guess about whether these things are breed characteristics or specific to your girl. Do you have access to a nice, steady horse you could ride to get back some confidence? Sometimes that helps as well. Some people say that longeing a hot horse will get rid of the excess energy, but with mine it only makes them hotter. I see no reason to longe as a regular thing, and the “lessons” it teaches are really not things you’d want her to learn anyway. To get her relaxed, you might try just walking her on a lead and do ground work, such as sidepassing, forward laterals, turn on the forehand/haunches, and such. She will be more likely to concentrate on the new stuff than thinking you want her to just run. 13 is young – my gelding was 22 when I restarted him, and my girl just turned 13. They can and will learn new things at any age.
This seems very disorganized and incoherent, but I do tend to babble. Sorry.
It is never the horse's fault