Is a wife divorced by her husband's statement to her, "If you do not do such-and-such, then go to your family," knowing that she did not hear him, and this applies in cases of intention to divorce, or lack thereof, or hesitation?

If the husband did not intend divorce, or was hesitant, then his divorce does not take effect due to the statement not being explicit and requiring intention. However, if he intended it and meant it, then the divorce takes effect if the wife does not do what the divorce was conditioned upon, even if she did not hear him, because what matters is what was issued by the husband.