What is to be done, and what should the sister and her husband do, given that he is involved with another woman and refuses advice, even after she resorted to her brother?

The man must repent from his unlawful relationships with women and abandon them immediately. The wife should continue to advise him with kind words and effective means. If you are able to advise him, then do so, for "religion is advice." Do not abandon advising him due to your assumption that he will not respond. The wife must not fall short in fulfilling her husband's rights and should adorn herself for him to deter him from the unlawful.