What is the ruling on a wife spending the night at her husband’s family home with the husband’s intention for her to be like his mother and sister, knowing that the wife only found out about this later, and is the husband’s action of not approaching her considered a sin?

The statement: "If my wife spends the night at her mother's house, she is to me as the back of my mother" is a contingent ẓihār, and it takes effect upon the occurrence of the contingency. If you intended to make the ẓihār contingent, and your wife spent the night at her mother's house, the ẓihār has occurred. However, if you intended to prevent her and did not intend ẓihār, and she spent the night there without knowledge of the contingency, then ẓihār does not occur, based on the opinion of those who do not consider it to take effect if the contingent act is done out of ignorance or forgetfulness. One must avoid such phrases because ẓihār is forbidden.