How can one return to his wife after he informed his family that he is "angry with her and that she is divorced," without informing her, and does that require a new marriage contract?

If you pronounce a divorce upon your wife, she is divorced, even if she is unaware of it. If this divorce does not complete the three divorces, then you have the right to take your wife back before her waiting period (iddah (definition)) ends. The waiting period ends after three menstrual cycles, or by delivering the baby if she is pregnant, or after the passing of three months. If the waiting period has ended before you take her back, you do not have the right to take her back except through a new marriage contract.