Instrumentation Amplifier input saturation problem
You have made several errors.

1) You have become deeply confused about what grounds do. For instance, with power supplies of 0V, 6V and 12V, you nonetheless refer to " output is 0V to neg rail", suggesting that you are using your "6V" power input as "0V" for signal purposes. This is certainly possible, but at some point you need to tie your "grounds" together. Just using capacitive coupling won't save you if your analog signal ground is bouncing around with respect to the ground of whatever device this thing is feeding.

2) You cannot feed an op amp with a bare capacitor. In your case, since "6V" is your equivalent signal ground, you should try







simulate this circuit &ndash; Schematic created using CircuitLab

and Tony's comment about reducing your cap values is probably wise.

3) Finally, and this is critical, R1 pin 4 should go to U1.3 pin 9, not pin 10.