If your parents absolutely refuse to let to rehome the platy, you will have to keep it.
Hard water is water that contains a lot of calcium and magnesium. Fish which come from hard water have evolved so their bodies excrete most of these minerals. When they are put in soft water, they continue to excrete them but as there aren't many minerals in soft water, they can't take up enough to replace the amount they excrete. This causes physical stress, which results in a lowered immune system and the fish is more susceptible to disease.
What this boils down to is the platy won't live as long as it would in hard water. But if you are not allowed to rehome it, just make sure you give it as good a life as you can.
Hard water is water that contains a lot of calcium and magnesium. Fish which come from hard water have evolved so their bodies excrete most of these minerals. When they are put in soft water, they continue to excrete them but as there aren't many minerals in soft water, they can't take up enough to replace the amount they excrete. This causes physical stress, which results in a lowered immune system and the fish is more susceptible to disease.
What this boils down to is the platy won't live as long as it would in hard water. But if you are not allowed to rehome it, just make sure you give it as good a life as you can.