Is my sister-in-law's husband cheating on her?

The nature of the betrayal is not clear. If what is meant is engaging in an illicit relationship, then it is a reprehensible act forbidden for a Muslim to do. The prohibition is confirmed and the sin is magnified if the man is married. The duty is to advise him and remind him of Allah, and to threaten to expose his affair if he does not desist. If what is meant is the man marrying another woman, then that is not betrayal; rather, it is a permissible matter if he is capable of being just.