Tania Clarence is accused of three counts of murdering a child aged over one year old between April 20 and April 23 this year.
No formal plea was entered and Mrs Clarence was remanded in custody.
Chairwoman of the bench Fiona Abbott said: "For these three charges you will be sent to the Central Criminal Court at the Old Bailey for a preliminary hearing on 9 May.
"There will be a bail application at the Central Criminal Court at 10am on 29 April."
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Cloud and outbreaks of rain will ease away eastwards during the morning, clearing the east coast around midday with sunny spells developing.
Police and emergency services are attending the scene.