Either “The life of your parents IS in your hands” or “The liveS of your parents ARE in your hands” would be correct. The number (e.g., singular or plural) of the verb “to be” (e.g., “is” or “are”) has to agree with the number of the noun that is the subject of the sentence: here, that noun is “life,” which is singular. Even though “parents” is plural, “parents” is not the subject of the sentence; rather, “parents” is just part of the adjective phrase “of your parents” that modifies the subject noun, “life.”