Is saying, "By Allah, if my wife does this, I will send her to her family's home, and after that, she won't know me, and I won't know her," considered a divorce, knowing that the questioner has not yet consummated the marriage with his wife?

This phrase does not result in divorce; it is merely a promise of divorce upon the fulfillment of a condition. Divorce does not occur by merely promising it, nor is one obligated to fulfill such a promise. Therefore, no divorce takes place for the wife with this phrase, whether she performs the suspended action or not, and there is no need to inform her about it or ask her about its occurrence in this matter.