Tareena Shakil, 26, told her family she was leaving for a holiday in Turkey in October 2014 but instead travelled to the city of Raqqa, the de facto capital of IS in northern Syria, Birmingham Crown Court was told this week.
She is believed to be the first British woman to return from the IS heartland to face terror charges.
"Although she booked a return flight, she was not going to come back, and this was no spur-of-the-moment decision," prosecutor Sean Larkin told the jury.
"She was given a house to live in. She was provided for. She was given access to firearms, and there were images of her child wearing clothing with the IS logo
Shakil was arrested by British police at Heathrow airport in February last year after arriving on a flight from Turkey.
She told officers she was kidnapped and taken to Syria but had managed to escape. The prosecution believes that was a lie.
In a message to her father, who was back in the UK, she allegedly wrote: 'I can leave, but I don't want (to). I want to die here as a martyr.'
She also told her family: 'If you don't love ISIS I don't want to talk to you anymore.'
Her defence lawyer, Timothy Moloney, told the court: "Her marriage had ultimately broken down and she accessed websites about life in Syria. The issue is whether she intended to encourage terrorist acts or was reckless. Her case is that she did not and was not reckless. The second issue is whether she became a member of IS and her case is that she did not." Shakil's trial is expected to last three weeks.
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