Aaron Gilsenan (41) claimed he was unaware the children, aged four and six, were in the car when he took it from Ninthlock Road in Clondalkin on Monday afternoon.
The girl told her father "we were kidnapped and he was asking for money", a court heard.
The children were "extremely frightened" by the ordeal, a garda witness said.
It is further alleged that Mr Gilsenan went into a nail salon, while still with the children, and tried to take the till, but was challenged by staff and left.
Judge David McHugh refused bail and remanded Mr Gilsenan in custody to appear before Cloverhill District Court on Friday.
The accused, with an address at St Mark's Gardens in Clondalkin, appeared before Blanchardstown District Court charged with child abduction, unauthorised taking of a vehicle and criminal damage.
Garda Amy Morrissey objected to bail, citing the seriousness of the charges and the strength of the evidence.
Outlining the allegation, Gda Morrissey alleged Mr Gilsenan entered the Moldova store on Ninthlock Road shortly before 2pm on May 30 and demanded that staff open the till.
Gda Morrissey said Mr Gilsenan, who did not wear a face covering, led staff to believe he had a gun.
She alleged he pushed a staff member to the ground, and staff were in fear for their lives.
Mr Gilsenan left the shop, and made off in an Audi A5, which was parked outside, she said.
The driver had briefly left the car, and his two children, aged four and six, were in the back seat.
Gda Morrissey alleged that Mr Gilsenan then went into Nail-Kandi, and tried to pull the till out of the wall. However, he was challenged by staff and he left the scene.
Gda Morrissey said Mr Gilsenan had the car at the time of the Nail-Kandi incident.
She said Mr Gilsenan was apprehended by gardai on Neilstown Road, and the two children were in the back seat.
The accused was not known to the children or their father, she said.
Gda Morrissey alleged the little girl told her dad: "We were kidnapped and he was asking for money".
The garda said Mr Gilsenan was interviewed by gardai, and he made admissions. He also admitted he was addicted to heroin and crack cocaine, and was spending between €100 and €200 a day on crack.
Gda Morrissey told the court the children were "extremely frightened" by the ordeal but were physically unharmed.
Defence lawyer Ciaran MacLoughlin said Mr Gilsenan was willing to abide by any bail conditions.
Mr MacLoughlin said Mr Gilsenan was unaware the children were in the car and his intention wasn't to take them.
However, Gda Morrissey alleged Mr Gilsenan could have stopped at any time, but he "went on a spree".
Judge McHugh said he was refusing bail and he remanded Mr Gilsenan in custody until Friday.
The accused has not yet indicated how he is pleading to the charges.