Does a divorce occur if a man swears to his wife: "You are forbidden to me as my sister is forbidden to me" (with doubt about his saying: "You are divorced from me") if she brings certain foods for their children until the end of next month, and then the wife, forgetting, gives her children a sum of money with which they buy these foods before the specified period expires?

As long as you are doubtful about uttering the divorce (talaq (definition)), the divorce does not occur due to your breaking of an oath, because divorce does not take effect with doubt. As for your statement: "You are forbidden to me just as my sister became forbidden to me," this is a conditional ẓihār, and breaking it depends on your intention. If you conditioned the ẓihār on her bringing food by any means, and your wife did so forgetfully, then there is no breaking of the oath upon you, nor is there expiation. The fatwa (definition) (religious edict) we adhere to is that if one fulfills the condition of a conditional oath forgetfully, there is no breaking of the oath upon them. We also caution you that swearing by forbidding one's wife is an objectionable and impermissible act. The permissible form of oath is swearing by Allah Almighty.