The 34-year-old, who cannot be named, is charged under the Child Abduction Act 1984 with taking two children out of the UK from Heathrow Airport on 10 October.
Appearing at Leeds Crown Court via videolink, the woman was remanded in custody. No formal pleas were entered.
At the short hearing, a further court appearance was set for 17 November.
Judge Sally Cahill QC said: "These are extremely serious offences and you are facing a custodial sentence".
A woman from Bradford accused of trying to take her children to Syria has been warned she may be jailed.