IMHO, every western horse can greatly benefit from proper reining training, she may never be a great reining horse, but she could be decent with proper training. It puts an excellent foundation on them for whatever else you may want to do. HOWEVER, reining is something that should really be taught by someone experienced in the discipline. Because of the high-torque, high-stress aspects of some of the maneuvers, it is very easy to injure a horse if they are taught to do it wrong or if they are asked to do it too often. People who aren't experienced in training for a certain discipline (or training in general) will often ask the horse to perform a certain maneuver over and over and over until they get it "perfect". That's incorrect and puts a lot of additional wear and tear on their bodies.
As for a sliding stop, there is much more to it than just stopping hard. A horse has to supple their face, round their back, tuck their hind legs up underneath them, and continue forward motion with their front legs. You're going to need some help to put the beginnings of a good stop on your horse, she is eons away from being ready to start trying to slide. She stops decently hard but she does not stop well. She flings her head and braces against the bit (my guess would be because you are fairly quick with your hands), she stops with all her weight on her front end and her hind end just kind-of flops around behind her. That's what causes her stop to be so jarring.
If you are serious about getting into reining and being competitive, even at lower levels, or even if you just want to advance her training through reining, then you are going to need some serious help from a knowledgeable trainer.