Does a divorce occur if a man tells his wife, "Go to your family and sleep there," intending to threaten her, not to divorce her, given that he has repeated this statement before?

If you did not intend divorce by the phrase "Go to your family," then it does not constitute a divorce, because it is not an explicit declaration of divorce but rather one of the allusive expressions that require intention. The correct view is that it is among the subtle allusions. Therefore, do not worry and do not succumb to whispers [of doubt].