It is easy to connect LabVIEW to multiple instruments or multiple instances of the same instrument, but you typically need a LabVIEW Driver that has a Session or Instrument parameter to specify which you want to use (I'm currently working with 24 Stations consisting of a Balance outputing a serial stream to a VISA port and a IP Camera taking videos, all 24 running simultaneously).
However, I haven't heard of a "Picoscope" nor have I seen any Picoscope drivers in LabVIEW. You've also shown us none of the code you are using, so I have no idea how a Picoscope connects to LabVIEW.
Bob Schor