Forwarding serial output from a Nano to Uno that's used as the ISP
As Chris Stratton suggests in his comment above:


  You can't really connect an ordinary Arduino's serial pins to both another device and the on-board USB serial converter at the same time. 


To solve your serial monitor problem use a separate USB serial converter and connect that to your Arduino Nano.

If you don't have access to a dedicated USB serial converter you could use software serial on the Arduino Nano. This allows you to connect the Arduino Uno Rx pin to the software serial Tx pin. You will also need to program the Arduino Uno with a program that re-transmits the data it receives back out to the PC serial monitor.