I agree she should be looked over for any damage to her back. Vets here have portable X-ray machines, but palpating her might also reveal sensitive areas that need readjusting. Maybe you should bring in a chiropractor.
I was the same as you as a child - parents knew nothing about horses, but bought me a horse anyway and let me just do my thing. It worked out somehow, but I wasn't a very good horse owner then. Things are different now, we know more, and that means we have an obligation to apply that knowledge to our equine friends.
You may want to look at saddle fit too. We have a short-backed Arab with a fairly sprung rib cage, and he is very, very hard to fit. My daughter rides English and we've had great luck finding saddles from British makers (they are often made for ponies so they have short backs and round barrels). I'm not familiar with Western brands as much (I assume you're talking about a Western saddle since you used the word "cinch"). If you have access to a saddle-fitter, that's the quickest and easiest way to figure out what your horse needs. If not, take wither tracings and send them into some saddlers. Even if you don't want to buy one of their new, expensive saddles, once they tell you what size you need, you can start looking for used models if that's your preference.
Remember though that horses shouldn't carry more than 20% of their weight. Some horses can carry more of course, but some cannot. Be careful of letting just anyone on your daughter's horse in the future.