The 34-year-old woman, from Bradford, West Yorkshire, cannot be named for legal reasons but pleaded guilty to two charges of abducting children under 16.
Judge Rodney Jameson QC said she would be sentenced on 8 January.
The woman and two children had flown from Heathrow to Turkey on 10 October, Leeds Crown Court heard.
She was planning to travel on to Raqqa in Syria.
However, the woman was arrested after landing in Istanbul, Turkey, with Â£4,000 in cash after her suspicious husband alerted police.
She had told her husband she was taking the children to a birthday party.
She later admitted to police she had planned to travel to Syria and ultimately to Mosul in Iraq though did not tell family as they would not approve.
The defendant was born in the UK and spent her formative years in Pakistan before returning to live in Bradford.
Earlier this year her family noted she was becoming "more overtly religious" telling them she wanted her children to grow up under Sharia law and she wanted to give up her job in finance as charging interest on money was "un-Islamic", the court heard.
The woman's lawyer, Marie Harbin, said she was a "loving, caring mother" who was "not a supporter of Islamic State, the organisation itself" but wanted to live in a state which follows Sharia law.
Judge Rodney Jameson QC replied: "It's a fairly narrow distinction."
The women could face up to seven years in jail.
A mother who tried to take her children to Syria to live under Sharia Law faces a "substantial custodial sentence", according to the judge at her trial.