The 14-year-old from Blackpool disappeared on 1 November 2003. Her body has never been found.
Karen Downes said she is taking legal action over a 13-year gap in releasing CCTV images of the teenager's last day alive.
Lancashire Police has declined to comment.
She said the footage that detectives released in 2016, 13 years after she went missing, could have helped solve the case had it been available earlier.
"They had [the CCTV] for 13 years," said Mrs Downes. "It shows Charlene in the town that afternoon in the same clothes she disappeared in.
"If they'd have shown it before... who knows?
"We have suffered all these years not knowing where she is."
She said police "need teaching a lesson".
"It is not about the money. I want to force the police to do their job," she said.
"If I got money I would get something for Charlene like a memorial."
Charlene is shown in the CCTV with her sister Rebecca on Bank Hey Street walking towards the Coral Island amusement arcade.
She went home but returned to Blackpool town centre later that evening - the last time she was seen.
A judge cleared a man of Charlene's murder in 2008 after "grave doubts" were raised about evidence during his second trial. The jury in his first trial failed to reach a verdict.
In 2009, the Independent Police Complaints Commission (IPCC) said police evidence-gathering errors contributed to the retrial's collapse.
The IPCC found strategic and tactical failure in the management of the material and several officers were disciplined, one forced to resign in 2011.
But this resignation order was overturned by a 2012 Police Arbitration Tribunal.
The mother of missing teenager Charlene Downes said she is going to sue police over mishandling her murder case.