A woman got out of the vehicle and an unknown man jumped in and took the car.
Police said it happened at Boucher Crescent in south Belfast at about 17:25 GMT.
Members of the public managed to stop the car but the man fled on foot.
A short time later a man in his 30s was arrested and remains in custody. The two children were unharmed.

In total, 99 were seized by police under the Dangerous Dogs Act, down 60 from 159 in 2015.
Figures were obtained from all Welsh police forces using a request under the Freedom of Information (FOI) Act.
National Police Chiefs' Council spokesman Deputy Chief Constable Gareth Pritchard said many people bought dogs without knowing their temperament.
North Wales Police said attacks rose from 158 to 246 in the area. In south Wales, it went up from 298 to 332 and in Dyfed-Powys' area the numbers increased from 45 to 53.
Gwent Police recorded number decreased from nine to three, in the figures obtained for BBC Radio Wales' Jason Mohammad Show.
Dep Ch Con Pritchard, who also works for North Wales Police, said: "We are concerned people are buying them on the internet.
"They are buying at car boot sales and buying at motorway service stations.
"They are not seeing the dog in its environment and understanding its temperament."
He added that if people are thinking of buying, they should "see the dog with the mother, see the temperament and understand the power and the attributes of the dog".
Despite the increase in attacks, the same FOI figures show the numbers of seizures under the Dangerous Dogs Act have fallen from 159 to 99.
In North Wales Police's area, the figure went down from 32 to 16, in south Wales, from 113 to 72, there were two seized in 2015 and 2016 in Gwent and in Dyfed-Powys, the figure dropped from 12 to nine.
Jayne Dendle, from Swansea, is a member of the campaign group Born Innocent, that lobbies against the Dangerous Dogs Act.
"Owners can just go out and buy any puppy, everything is totally unregulated and people don't necessarily see a dog as a lifetime pet and don't put the effort and energy they need into it," she said.
"Socialising it and exercising it. A dog is a big commitment and we need to put a great deal of time into that."

The 37-year-old midfielder announced his decision after playing the whole match as Greece lost on penalties in the last-16 tie against Costa Rica.
"This was my last game for Greece," said Karagounis.
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"We wanted to stay in Brazil another week or even longer but you can't change it now."
Karagounis made his international debut in 1999 and amassed a record 139 caps for his country, scoring 10 goals in the process.
He helped Greece win Euro 2004 and their progress in Brazil meant they reached the second round of the World Cup for the first time in their history.
Karagounis, who was released by Fulham at the end of last season, said he was making way for Greece's next generation of players.
"The national team has grown up, younger players have won invaluable experiences," he added.
"This is no small thing and as we helped the team come of age we hope it will continue to be as successful in the future."
Greece coach Fernando Santos will also leave his post after his contract expired on Monday.
Santos was sent to the stands before the penalty shootout took place against Costa Rica and had to watch on television as his side made their exit from the World Cup.
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A man has been arrested after a car was stolen with two young children inside.
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There were 634 reported dog attacks in Wales in 2016, up by 124 from the year before, according to latest figures.
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Greece captain Giorgos Karagounis has retired from international football following his country's elimination from the 2014 Fifa World Cup.