Instrumentattion amplifier gain appears to change
Most likely the common mode level of the instrument output is not in range for the in-amp input.

First you should ensure your two circuits have a common ground.

Then you should make sure the instrument common mode voltage is within the recommended range for the in-amp input. If the instrument output is biased near ground, the easiest way to do this might be to use a negative supply for the VS- terminal of the in-amp.


  In the figure, there is a cylinder-shaped symbol around the signal input. I don't know exactly what this is,


That's a shield around the cable connecting the inputs of the in-amp to whatever source they're measuring. 

If the connection from your instrument to the amplifier is short, you may not need it.