What is the ruling on swearing not to travel with one's mother and family again, with the intention of anger?

If you intended to swear an oath and your tongue slipped into an oath of anger (yamin (definition) al-ghadab), then it is a binding oath for which expiation (kaffarah (definition)) is due if you break it. The majority of jurists hold that an angry person is accountable for what he says and does, including oaths. So, if you believe that traveling with your family is better for you, then travel and offer expiation for your oath, based on the Prophet, peace and blessings be upon him, who said: "Whoever swears an oath and then sees something better than it, let him do that which is better and offer expiation for his oath."