Is the mother entitled to custody of her son and to travel with him to Jordan, given that the father owns a house and has a stable income, and the mother is employed?

Your brother's wife is not allowed to travel with her ward for permanent residence outside the country of the ward's guardian. If she does so, her right to custody is forfeited forever, and the guardian has the right to take the ward from her. A condition for the custodian's custody is that she does not travel away from the country of the free guardian concerning the free ward.