Bernadette Romulo has lived in Australia for the past 11 years, but fears she and her two daughters will be sent back to the Philippines after her permanent residency application was rejected.
However her eight-year-old son was born in Australia to an Australian father, who has partial custody.
Mr Dutton is unlikely to intervene, but lawyer Angus Francis says Ms Romulo's case deserves special consideration, particularly as it involves allegations of domestic violence.