What is the ruling of Islamic law regarding a man divorcing his wife over the phone in a moment of anger, then taking her back after accusing her and casting doubt on her honor, knowing that she added her sister's husband on "Snapchat"?

Jealousy in situations of suspicion is commendable, but one should have paused and handled the matter with wisdom to avoid dispute and divorce, especially since you are at the beginning of your marital life, and Satan seeks to separate spouses. Divorce during menstruation is an innovated divorce (bid‘i), but it is valid according to the majority of scholars. Since the wife has been taken back, it is advised to lay down foundations for your interactions to stabilize your marital life.