Mary McCann, 35, of Bamford Avenue, Derby, failed to appear at Aylesbury Crown Court to answer two charges of causing death by dangerous driving.
Her 10-year-old son Smaller and four-year-old daughter Lilly died after a collision with an HGV near Milton Keynes on 9 August.
Judge Francis Sheridan said he wanted ports and airports on alert for her.
"It is most likely she will flee to Ireland," he said.
"This is a sad case, but by absconding to avoid the indictment being put is in my view tactical."
The family's white Vauxhall Astra collided with an HGV between junctions 14 and 15 of the northbound carriageway at about 23:10 BST.
Ms McCann and another child passenger were injured.
A family member said they were on their way back from a party in London and Ms McCann's 13-year-old daughter had stayed in the city.
Prosecutor Heather Stangoe told the court: "Unfortunately, we do not know where she is. We were informed through her solicitor that they had failed to make contact with the defendant. Her bail address was her sister's and she is not there.
"It was the funeral of her children this week. Her one-year-old child is with the grandmother and is safe."
Defence barrister Laban Leake said: "The funerals were on Monday and Tuesday.
"She gave a telephone number, an attempt was made to contact that number, but there was no response.
"We know nothing of her state of mind."