My question involves a child custody case from the State of: CO

I have a friend of the family who is an illegal alien and has unofficial custody of his three daughters who all were born in the U.S. The mother, who is also an illegal alien abondoned them about a year ago. She moved out of state but is coming back into the state and threatens that she will take the father to court for custody. Is this even possible? Can two illegal aliens have a custody battle for these U.S. born children in a American Courtroom?