Throwing shot and disc, should not have any ill effects on a pitchers pitching, Both shot and disc, develop fast twitch muscle fibers which can only help a pitcher, speed and explosive power, is just what we want out of a pitchers stride.
The shot is a hard drive of the legs, with the power coming from the speed of the stride across the circle and the hip rotation, the arm is just a fulcrum to push the shot. The same is true of the disc, the throw comes from the speed of the rotation,the push off the leg, and the arm whip, which is led by the hips , much like batting. the arm is again the fulcrum that holds the disc, that is all it really does.
There is an explosive wrist snap involved in the shot that really only putters know about.
As far as juggling two sports , thats up to your school.
Shot and disc will only make a pitchers stride more powerful, it will do nothing to hurt her speed ,control or mechanics, and will certainly not hurt her wrist snap. If anything it would give her better body awarness, and an understanding of where power and speed are generated in her pitching motion.