Fiona Adams, 24, was found not guilty by a jury at Nottingham Crown Court of murdering daughter Niamh, five, and two-year-old son Cayden in the blaze in Buxton, Derbyshire.
She escaped from the house in Edale Way with youngest child Kiernan by jumping from an upstairs window just before midnight on April 23 last year.
Speaking outside Nottingham Crown Court, where a jury cleared her of murder, arson and grievous bodily harm, Ms Adams said she was happy with the verdict.
A statement said: “Fiona will be most grateful if the press and public will now give her and her family time to pick up the threads of their lives and establish some kind of normality.”
During the trial, prosecutor Timothy Spencer QC told the court Adams started the blaze because she wanted to create a “drama” to get the attention of her then partner, James Maynard.
The court heard Mr Maynard, who is the father of all three children, had cheated on her several times, which led to her attempting suicide on a previous occasion. Speaking after the verdicts, Mr Maynard, who is no longer in a relationship with Miss Adams, said he never doubted her innocence.
Miss Adams’ father Michael vowed not to stop fighting until Niamh and Cayden’s killer was caught.
When asked who he thought was responsible for the fire, he said: “I’d love to give his name, but he’s a known arsonist who went missing two days after the fire and the police still haven’t found him yet.
Derbyshire Police said in a statement that, in light of the verdicts, the force would appoint an independent team to review the case.