Are the phrases "Go to your family, and I will send your divorce papers after you" and "Take your daughter, I don't want her" considered a divorce? And is her return to the marital home before she went to her family, and speaking with her over the phone, considered taking her back, especially since her father is preventing her return?

Your statements to your wife, "Go to your family," and to her mother, "Take your daughter, I do not want her," are implicit divorce declarations (kinayah) that result in divorce if you intended it. If you intended divorce with both statements together, then two divorces are counted, and you may take your wife back if you have not divorced her before. If you intended divorce with only one statement, then one divorce is counted, and you may take her back if you have only divorced her once before this.

Merely returning your wife to the house without uttering the word of return (raj'ah) or intimate touching with desire does not count as a raj'ah. However, if there was intimate touching with desire and the intention of raj'ah, or if you verbally expressed the raj'ah, then the raj'ah is complete. If you have not taken her back, you may do so now by contacting her and explicitly stating the raj'ah, or by verbally expressing it, as long as her waiting period (iddah) has not expired. The iddah is three menstrual cycles for a menstruating woman, three months for a non-menstruating woman, and the delivery of the baby for a pregnant woman.

It is permissible to strike one's wife within Islamic guidelines. If you had taken her back before the expiration of her iddah, she is your wife. Her father's prevention of her return is a sin, and it is forbidden for him to prevent you from seeing your daughter. It is not permissible for your wife to abandon her home without your permission, nor is it permissible for her to obey her father in this regard.

If the iddah has expired, the raj'ah is not valid, and a new marriage contract is required with a guardian (wali), two just witnesses, and a dowry (mahr). If her father refuses to renew the marriage despite her desire, the guardianship transfers to the next in line of guardians, or to the Sharia judge, or to a righteous Muslim man with her permission.