What is the ruling on saying "By divorce, you are not going to the gardens at my family's," with the intention of preventing the wife from going? Does this divorce take effect and count towards the three divorces, and what is its expiation?

An oath of divorce falls under the category of conditional divorce according to the majority of scholars. If the condition is met, the divorce takes place. Sheikh al-Islam Ibn Taymiyyah held the view that its expiation is merely the expiation for an oath, but the view of the majority is the more preponderant.

If you intended that your wife should never go to the aforementioned place, then her going there triggers the divorce according to the majority of scholars.

If the divorce occurs, you may take her back before her waiting period (iddah (definition)) expires, provided it was the first or second divorce. A re-marriage (raj'ah) does not require a new contract or witnesses, and it occurs through speech or action with the intention, and through sexual intercourse even without intention, according to the soundest opinion.

However, if you intended a specific time, or a particular manner of going out, and that ceased to be the case, or she went out in a manner different from what you swore by, or if the reason that prompted you to take the oath was a specific cause and that cause no longer exists, then divorce does not occur by her going out due to the non-fulfillment of the condition for breaking the oath.