Probe into gay adoption row
Chief social work officer at Edinburgh City Council, Michelle Miller, will reportedly lead an investigation into the complaint.
A city council spokesman reportedly said officials had received the family's complaint and it would be assessed by Miss Miller and a team of staff dedicated to dealing with public grievances.
The family are expected to discuss a legal fight, bankrolled by an unnamed Scottish millionaire, with lawyers later in this week.
The council has 28 days to review the complaint.