During a five-minute hearing she spoke to confirm her name, date of birth and address, at Whernside in the city.
No pleas were entered to either of the charges she faces. A brief outline of the allegations was provided by prosecutor Peter Conroy, who told magistrates that the man and child had each suffered stab injuries to their necks.
The case was adjourned by magistrates and she is next due to an appear at Carlisle Crown Court for a plea and trial preparation hearing on 24 June.
No bail application was made and Ms Mounsey has been remanded in custody until her next court appearance.
