Christine Connor was charged after explosive devices were thrown at officers responding to an emergency call.
The pair were targeted as they got out of their vehicle in the Ballysillan area of the city in the early hours of Tuesday 28 May, but escaped injury.
Connor, 27, appeared before Belfast Magistrates' Court on Wednesday charged with two counts of attempted murder, possession of pipe bombs with intent to endanger life, and preparation of terrorist acts.
A judge granted an application for her address to be withheld after being told of paramilitary threats and attacks on a previous family home.
Wearing a denim jacket as she entered the dock, Connor waved to her mother and a man sitting together in the public gallery.
She did not respond or acknowledge the court when asked if she understood the charges against her.
Defence solicitor Michael Madden claimed the police case contains "significant evidential difficulties".
However, the lawyer confirmed he was not in a position to seek bail at this stage.
Seeking the ban on publication of his client's address, Mr Madden cited her mother's right to life under European law.
He said the family was notified by police in 2007 that paramilitaries had details of cars and their house.
Windows were smashed and vehicles attacked at the time, the court heard.
Mr Madden said the threats stopped once Connor and her mother moved house.
District Judge Fiona Bagnall granted the application on the basis of the perceived risks to the family.
She said: "In the circumstances I don't think it's a big leap to say disclosure through these proceedings may lead to danger, particular to the mother."
Judge Bagnall added that Connor could be named and described as being from north Belfast.
The accused was remanded in custody to appear again next month.