A court heard the 34-year-old Bradford woman fled the country after telling her husband she was taking the youngsters to a birthday party.
Police were alerted on October 10 this year after the husband became suspicious of his wife’s behaviour.
Inquiries revealed that she had boarded a flight from Heathrow to Istanbul and she was arrested later that day by Turkish authorities when the plane landed.
Leeds Crown Court heard the woman was returned to the UK and admitted to police that she had planned to take the children to live in Mosul, Iraq.
The woman pleaded guilty to two offences of abduction of a child when she appeared before the court today.
Andrew Semple, prosecuting, said the woman had the children to her first husband and did not seem particularly religious.
They divorced and she married her second husband in 2013. Mr Semple said she told her husband in August this year that she wanted to give up her job and and appeared more “overtly religious”.
The prosecutor said: “She said she wanted to bring her children up in a country with Sharia law”
Mr Semple added: “She contended that there was only one county - Islamic State.”
The court heard that the defendant’s younger brother left the UK to live in Mosul and she had been in contact with him on a mobile phone.
Mr Semple said the woman had put plans in place to leave the county by late September and had suitcases packed.
The day before she left the country her husband had become increasingly suspicious and took the opportunity of looking at her phone.
The phone revealed contact with an individual which discussed going to Istanbul, Raqqa and Mosul.
The court heard the woman’s suitcase was found to contain £4,000 in cash after she was arrested.
When interviewed on her return to the UK she told police she had had become interested in moving with her children after her brother had left the country.
She said she planned to meet with her brother after taking her children to Turkey and then they would cross the border together into Islamic State territory.
Marie Harbin, mitigating, told judge Rodney Jameson, QC: “I have spoken to her at length about why she has ended up before the court.
“She does have beliefs that your honour or I might deem inappropriate but she wishes to point out that she is not a supporter of ISIS itself, but of Sharia law.
“She did not want to take her children to support a terrorist organisation but wanted her children to be raised under a regime that was more appropriate.”
Miss Harbin said the woman’s brother had portrayed an image of Iraq as something that was “idyllic”.
She added: “She also viewed a number of videos online which in effect can be viewed as propaganda.”
Judge Rodney Jameson adjourned the case until January 8 when the woman will be sentenced.
The judge described the case as having “an important national dimension” and said he wanted to consider details of similar cases prosecuted in the UK this year before passing sentence.
The woman was remanded in custody until the next hearing. Judge Jameson added: “A substantial custodial sentence in inevitable.”