Rebecca Minnock, 35, and son Ethan, three, disappeared from their home in Highbridge, Somerset, on 26 May.
The next day a district judge ruled Ethan should live with his father.
Det Ch Insp Marie Wright told BBC Points West she was worried about the "emotional impact" on Ethan and his mother of weeks in hiding
"Rebecca needs to return Ethan back to the court process where he is going to live with his father," she said.
"Rebecca knows this and she is evading the court process."
She added that she did not believe Miss Minnock was still in Somerset and police had received reports she had been seen in Cheltenham and, more recently, in Birmingham. The BBC's Steve Knibbs said he understood the police search was now focusing on Birmingham.
"Ethan's father is very upset, as you would expect. Ethan needs to go and live with him," Det Ch Insp Wright told the BBC.
On Sunday Miss Minnock's brother, sister and mother were arrested, accused of withholding information.
They told a judge at Bristol Crown Court they did not know her whereabouts - he said he had suspicions they knew more but released them from the court, saying he was "not satisfied" he could commit them for contempt of court based on the evidence he had heard.
Miss Minnock is about 5ft 3ins tall, of medium build, with dark wavy shoulder-length hair, and Ethan has blond hair and blue eyes, police said.
He has lived with his mother since his parents separated in February 2013.
A month later, his father Roger Williams, applied for contact with him.
On 27 May this year a district judge ruled Ethan should live with his father after finding Miss Minnock had made false allegations and obstructed contact between the father and son.
This week reporting restrictions were lifted in an effort to find the pair.
A mother and child who went missing two weeks ago in a custody battle may have been spotted in Cheltenham and Birmingham, say police.