If the princess appears it would be the first time that a member of the royal family has attended in court in 100 years.
District Judge Terry English said the Princess Royal and her husband, Commodore Tim Laurence, must be at East Berkshire Magistrates' Court in Slough on 21 November.
The couple, who have been charged under the Dangerous Dogs Act, face a fine of up to £5,000 and up to six months' imprisonment if convicted.
They are accused of being in charge of a dog that was dangerously out of control in a public place.
Official business
On Wednesday the court heard that the couple's bull terrier bit the children, aged seven and 12, in Windsor Great Park on 1 April.
The alleged attack took place two days after the death of the Queen Mother.
Princess Anne's barrister Hugo Keith told the court she had been unable to attend Wednesday's hearing because she was on a charity visit to Ethiopia.
Mr Keith said: "One of the defendants is unable to be here because she is engaged on official business abroad.
"It's quite normal for the first day of a summons to be adjourned in the absence of a defendant. There are good reasons for this today."
Destruction
At the end of the 15-minute hearing the judge said: "The court will expect both defendants to be present personally (at the next hearing).
"They are not proceedings that can take place in their absence."
He also imposed reporting restrictions, banning the media from revealing the identities of the two children.
The case can be heard by magistrates, or the couple could opt for it to go to Crown Court.
Apart from the threat of imprisonment and a fine, the destruction of the animal could be ordered.
Judges also have the power to disqualify the princess and her 47-year-old husband from keeping a dog.
Princess Anne, 52, has made clear she does not want preferential treatment.