Is a rubber band being stretched and being broken kinetic energy changing to potential energy?

Not really. You are breaking it, so you are simply using your kinetic energy on it. However, using a rubber band like a slingshot is. While the rubber band is tight, it contains potential energy. You transferred your kinetic energy to it as potential energy. When you release the rubber band and it does work such as shooting a wad of paper, that is converting potential energy into kinetic.