Does a divorce take place if a husband tells his wife, "You will be unlawful to me, and I will treat you like my sister and my mother," if his intention is to refrain from having sexual relations with her as a punishment?

A husband's statement to his wife, "You will be forbidden to me" or "I will treat you like my mother and sister," is a threat of ẓihār and not an actual ẓihār. Therefore, nothing takes effect from it. However, the wife must repent to Allah for her disobedience (nushooz) and her refusal to share her husband's bed. The husband, in turn, should trust his family and not rush into anger and jealousy without cause.