Tegan Doidge, 19, spent all but £150 of the money before building contractor John Doidge realised it was missing and called in the police.
She was living rough in Ottery St Mary and Exeter, Devon, and was found with cannabis when she was tracked down and arrested, Exeter Crown Court was told.
Doidge, of no fixed abode, admitted burglary and was jailed for two months in a Young Offenders' Institution. She had originally received a community order but was resentenced after failing to carry out 120 hours unpaid work.
Her mother Melanie sobbed in the public gallery and was given special permission to visit her in the cells after asking the Judge:"Can I give her a hug?"
Judge Euan Ambrose revoked the earlier sentence after Doidge was taken back to court for the second time for breaching her community order.
The judge said he was reluctant to jail a 19-year-old who had committed no other offences but he had no alternative because she had failed to work with probation officers.
He was told it was not possible to put her on a tagged curfew because she is homeless and sofa surfing and staying with different friends each evening.
He told her:"In the language of past times, this is a short sharp shock to bring home to you the effect of not complying with this order but without crushing you or introducing you to a criminal lifestyle.
"Your community order was imposed for a burglary at your mother and father's house although you may have perceived it as more than a theft.
"It involved an appreciable amount of money, most of which was not recovered.
"You were made subject of a community order but failed to turn up for meetings or unpaid work on numerous occasions and the probation service have reached the end of the road with you.
"You have proved singularly incapable of fulfilling promises and the explanation for this is your chaotic lifestyle, living on friends' sofas."
