What is the ruling on divorcing one's wife if the husband had agreed with her that divorce would be the consequence for disclosing a household secret or instigating a problem, and this indeed occurred?

The divorce is binding because it is an explicit declaration. The statement about divorce occurring upon departure was merely a promise, not a condition for its enactment.

Therefore, the wife has been divorced. She can be taken back (revocable divorce) before the expiration of her waiting period (iddah) without a new contract, provided this is not the third divorce.

One must be careful about uttering words of divorce or similar phrases, whether in seriousness or jest, to avoid regret.