Samantha Baldwin, who went missing with her two children from Nottingham in March, drugged her sons and falsely claimed her father sexually abused them, says judge Jeremy Lea.
Baldwin and her sons Dylan, six, and Louis Madge, nine, went missing in late March and were found last week at Sherwood Hideaway holiday park.
A short time later, she was arrested on suspicion of abduction.
During the police investigation it was revealed that the mother-of-two drugged her children with sedatives and anti-anxiety treatments to try to prove their father was guilty of abuse.
Judge Lea said: "In my judgement I found that the father had not perpetrated sexual, physical or emotional abuse against the boys as alleged by the mother, or at all, that the allegations made by the mother were false.
"I also found that the mother genuinely believed that he had done so, but that her belief was irrational and that the evidence of abuse was unreliable."
He added: "I also made a finding that in order to try to prove her case against the father, the mother had caused the boys to ingest substances that would give rise to a positive testing for benzodiazepine products and zolpidem".
The boys are in local authority care.
Baldwin has been arrested on suspicion of abduction and bailed.