Is a person considered a cuckold, or is the sin lifted from him and borne by his parents, if he is unable to change the reprehensible matters surrounding him in his home, especially concerning his sister's hijab and dress, despite his attempts to rectify that?

Enjoining good and forbidding evil is an obligation. If the parents do not fulfill their responsibility of correcting their daughter, they have no right to object to someone else who does. You should continue to advise your sister gently and with tact, for the Prophet, peace and blessings be upon him, said: "That Allah guides one man through you is better for you than red camels." One who denounces evil is not a cuckold (dayyooth). The responsibility of correcting your sister falls primarily on her guardian. Allah, the Most High, says: "O you who have believed, protect yourselves and your families from a Fire." You should not leave the house, as your presence there might be a cause for good or for lessening evil, and your dutifulness to your parents might have a good effect on them. If your sister persists in her error, then abandon her if you hope for benefit from abandonment; otherwise, leave it.