What is the ruling regarding a man saying to his wife, "You are divorced," without forethought or intention, and in the context of discussing difficult living conditions, especially when he has three children?

If your tongue slipped and you uttered a divorce without intending it, then no divorce is incumbent upon you. However, if you intended to utter a clear divorce, it takes effect even if you did not intend its consequence, because it does not require an intention.