Is the wife considered divorced if she does not reform herself after the husband says: "Either you reform yourself, or your brother will take you with him," knowing that he did not contact her brother? And is this considered a conditional divorce?

Your statement to your wife: "I will now call your brother on the phone and ask him to come, and I will refer the dispute to him; either you mend your ways or he takes you with him," does not result in divorce, even if you intended divorce, because you did not make the call nor did you refer the dispute to him.

However, if you repeat this statement, and the call is made, and her brother comes, then if she does not mend her ways, and you intended divorce with your statement: "(or he takes you with him)," a divorce occurs. Otherwise, it does not, because this is among the indefinite expressions (kinaya), and divorce does not occur with an indefinite expression except with intention.