Training is actually exactly what you should do, anonymous. Consider also recruiting your melanistic tyrunt to help you, especially seeing as it’s clearly concerned about the well-being of your shiny. Begin with easy exercises (light strength training and practicing of techniques your shiny knows well), then advance to harder and harder techniques and exercises until your shiny tyrunt can defend itself. Once it reaches that point, it should be able to fight back. (Naturally, you should also teach your tyrunt to use force only when absolutely necessary and not to instigate fights itself.)
Of course, at the same time, you’ll need to teach your other tyrunt to heel. Train them to work together, with your shiny and melanistic tyrunt, and teach them to behave themselves when encountering something that excites them (in a negative way). By balancing your shiny’s training with heel training for your other tyrunt, you may be able to instill discipline and harmony among your team.
Best of luck, anonymous!