Instrumentation amplifier not rejecting common mode signals
There is a VERY high chance you are facing component tolerance issues with a discrete-base instrumentation amplifier


For ideal components the overall gain is 10.119 (gain POT == 0) 

This complication comes from how well matched the two 47k, 18k and 68k resistors are. EQUALLY the additional bias network tolerance &amp; balanced rail.

If the upper resistors are +1% and the lowers are -1% the issue starts to become clearer. A slight bias.



your bias network is a POT + your supplies will cause a bigger error.

Perfectly matched resistor network BUT +-1% on the POt and +-10V supply.



So depending on how big of an offset you are seeing, it will come down to component mismatch &amp; the bias pot will be the biggest source of offset