No you can't unless you pay for all the 6 berths.
For family cabin you will have to travel on AC Sleeper coach and its not available in Pak Business Express. AC Sleeper is currently available in Night Coach Express (Private By Shalimar Group), Tezgam, Khyber Mail
In Night coach express, for Rs 12000 you get 2 person cabin with attached washroom and your 2 kids under 10 will travel free.