Does the divorce take effect by saying "I have divorced my wife" to the father in a moment of anger and without genuine intention, while there are family disputes and the wife's desire for a separate home that the mother rejects?

It is the wife's right for her husband to provide her with independent housing. This must be provided if she demands it and the husband is able. This is not considered disobedience to the mother, because obedience is in what is right. You should be kind to your mother and explain your excuse. If you initiate divorce with an explicit statement like "she is divorced," then it is effective. However, if the wording is ambiguous and could mean divorce or something else, it does not take effect without intention. If you falsely claim to have divorced her when you had not divorced her previously, the Shafi'is and Hanafis hold that it does not take effect religiously (diyānatā), but it does legally (qaḍā'an) if the matter is brought before a judge. The Hanbalis, however, hold that it takes effect both religiously and legally.