Does divorce occur by saying, "If you do it again, you are not my wife," with the intention of preventing the wife from doing something, and is it permissible for the wife to do it later with the husband's permission without divorce occurring?

A man's statement to his wife: "You are not my wife" is a metaphorical divorce (kinayah talaq). Its ruling depends on the husband's intention. If he intended divorce by it, then it is a conditional divorce that takes effect when the condition is met, according to the majority of scholars. If he intended admonishment and threat, and did not intend divorce, then divorce is not binding on him; rather, it requires expiation for an oath (kaffarat yameen) according to some scholars. If his intention was divorce, a revocable single divorce takes effect immediately upon her doing that thing, and he can take her back as long as she is within her waiting period (iddah) and this was not the third divorce.