Will I be absolved of responsibility if I let my young female relatives use the Internet for chatting without supervision, even though I warned them and could not prevent the connection?

If you are the only one aware of the reprehensible acts committed by your female relatives, you must prevent them to the best of your ability. If cutting ties with them prevents this reprehensible act and does not lead to a greater harm, then it is obligatory for you to do so. Their annoyance is not considered a harm that permits abandoning the change of a reprehensible act, due to the Prophet (peace be upon him) saying: "Whoever among you sees a reprehensible thing, let him change it with his hand; if he cannot, then with his tongue; if he cannot, then with his heart—and that is the weakest of faith." It may become incumbent upon you to bring about change if you are the only one capable of doing so. However, if there is another way to prevent it, such as informing your brother or their guardian, that suffices you, while continuing to advise them and guide them towards obedience.