Does divorce occur in the three aforementioned situations, knowing that I did not intend divorce nor did I explicitly utter it in any of them, and is the third situation considered a divorce?

The majority of scholars hold that if a husband makes his wife's divorce conditional upon an event, he cannot retract it. If the condition is met, the wife is divorced, whether the husband intended to effect the divorce or merely to threaten. This is the fatwa (definition) we adhere to. Some scholars, such as Sheikh Ibn Taymiyyah, are of the view that if the husband intended to effect a divorce upon the fulfillment of the condition, he may retract the conditional statement, and there is no consequence for him. If he did not intend to effect a divorce, but rather intended to threaten or prevent, then divorce does not occur upon the fulfillment of the condition; instead, he is required to pay expiation for breaking an oath (kaffarat yamin (definition)).

Accordingly, the fatwa we adhere to is that if your wife said to your mother the words upon which you made the divorce conditional, then she is divorced by that. However, if you intended by your oath to prevent her from saying these words without your consent, then you do not break your oath if you speak to her after you have permitted her to do so. And if she went down to her family's house, in the manner upon which you made the divorce conditional, then another divorce has occurred.

As for your saying to your wife, "It is better that you do not return, and stay with your family," and similar phrases, these are implicit statements (kinayah) by which divorce does not occur except with intention. Since you did not intend divorce by them, it has not occurred.