Lauren Etchells, who is accused of child abduction by police in Canada, pleaded guilty to lying to immigration officials alongside her parents, when they arrived on the island together in a 13ft-boat last July.
Prosecutor Simon Crowder told the court that all three adults initially claimed they had arrived from France “with the intention of having lunch”.
“Together they were using Jersey in an attempt to avoid compliance with a Canadian court order,” said Peter Harris, the assistant magistrate.
Before she was caught by immigration authorities in the Channel Islands, Ms Etchells had been off the radar for three years after leaving Canada with her children and then-partner Marco van der Merwe, who had acted as a sperm donor to Ms Etchells and her ex-wife Tasha Brown.
She disappeared following the breakdown of her marriage and a custody dispute with Ms Brown.
Ms Etchells was convicted after a four-day trial at the same court in December of two charges of exposing a child to risk of harm.
Her parents have been convicted of two charges of aiding and abetting.
Mr Harris said: “The waters around Jersey can be very dangerous. Both children were exposed to a risk of harm.”
They were all given six-month prison sentences, suspended for 12 months, fined £500 and told they must also pay costs of £1,600 between them.
Sarah Dale, defending Ms Etchells, said: “As you heard throughout the trial, Miss Etchells believed that she and also her parents had taken all relevant precautions to ensure the safety of the children during the crossing.”
She said: “Ms Etchells’s children are the greatest importance in her life and whatever her motive for making that crossing, she was adamant that she would not do anything at all that she felt put them at risk or endangered them.”
While on the run, Ms Etchell travelled to England, France, the Netherlands, the Middle East and possibly to Spain and Portugal before ending up in Jersey, according to police.
She was sentenced alongside her parents, Brian Etchells and Angela Hardy, on Monday at Jersey Magistrates’ Court.
Additional reporting by Press Association