What is the ruling regarding a man who said to his wife and children, "By divorce, I will not eat with you again," and then he ate with them? Does divorce occur in this case? And if it does, what is the ruling?

The majority of scholars hold the view that divorce occurs if an oath of divorce is made and the condition for it is met. This is the established ruling. Therefore, if the man ate with his children, a divorce has occurred for his wife. If this was the first or second divorce, he may take her back as long as she is within her iddah (definition) (waiting period). However, if this was the third divorce, she has become irrevocably divorced from him, and she is not lawful for him until she marries another man and that marriage ends.