What is the optimal course of action with a husband who swore and pledged not to betray, but then it became clear that he is betraying?

It is forbidden for a man to establish a relationship with a non-mahram woman or to speak with her without necessity. This prohibition is emphasized for a married man, especially if he has pledged to his wife to avoid such interactions. If what you mentioned about your husband, regarding his phone calls and messages with girls, is true, then he is disobedient and negligent of your rights. We advise you to be patient with him and to counsel him kindly, reminding him to fear Allah, while also being a good wife to him, beautifying yourself, and filling his free time. If he persists in his behavior and the marital relationship deteriorates, and you fear neglecting his rights due to your aversion to him, then it is permissible for you to seek Khul'. A covenant with Allah is considered an oath, as Allah says: "And fulfill the covenant of Allah when you have made it, and do not break the oaths after their confirmation while you have made Allah, over you, a guarantor. Indeed, Allah knows what you do." The majority of jurists hold that a single expiation is required for someone who has sworn multiple oaths concerning one matter and then broken them.