Does a divorce take place if one swears an oath upon his wife that she will not contact her relatives, while being angry and having previously given her the power to control divorce, and does the divorce multiply with multiple contacts, and is it permissible for her to contact them from her husband's phone?

Empowering your wife to decide her own marital fate or delegating the divorce to her does not affect an oath of divorce. The majority of scholars hold that divorce occurs if you break your oath, whether you intended to effect a divorce or merely to threaten. Some scholars, like Ibn Taymiyyah, consider swearing by divorce as a threat to be like swearing by Allah, and it necessitates an expiation for an oath. The authoritative opinion for us is that of the majority. Therefore, if your wife contacts these relatives, a single divorce will occur, and the oath will be dissolved. The divorce will not be repeated with repeated contact unless the phrasing implies repetition. There is no difference whether she contacts them from her phone or your phone, unless you intended to prevent her only from her phone. The permissible oath is swearing by Allah the Almighty, and swearing by divorce is among the oaths of the dissolute.