Samantha Ford, 38, admitted the manslaughter by diminished responsibility of Jake and Chloe Ford, who were 23-months-old.
But she has denied murdering the children on Boxing Day last year.
The twins were found dead at their home in Castle Drive, Margate, the following day.
Mrs Ford had been involved in a collision with a lorry in the A299 Thanet Way.
When rescuers arrived at the scene, she told them to check home because her babies were there.
They were then found dead after police raided the Kent home.
A further hearing has been set for June 10, and Ford was remanded in custody.
She will face trial on June 24.
Prosecutor Ed Brown QC requested the court hearing on June 10, for the Crown to confirm if her guilty pleas can be accepted.
He added the Crown Prosecution Service had recently received Mrs Ford’s psychiatric report.
Brown said: “We the prosecution are meeting tomorrow to discuss the contents and the background of this case.
“Certain steps have to be taken and ultimately we are using for the decision to be communicated to my learned friend’s instructing solicitors and to the court of course by Wednesday the 5th of June.”
Husband Steven Ford watched on in court today.
Mrs Ford, wearing a black suit and white shirt, spoke only to confirm her identity and pleas.
After the killings, Mr Ford tweeted: “Daddy’s twins xxx my beautiful babies. I love you.”
In a later tweet, he said: “I want the world to see my beautiful babies.
“Jake and Chloe forever xxx.”