Instrumentation Amplifier - is it possible to have an output signal inverted, with respect to the supply voltage?
You should be able to do this.


Swap the input pins.
Connect the REF pin to +5 V.


(caveat: I haven't tried such high voltages on the REF pin myself, and I'm not specifically familiar with the INA126)

In order to be sure of getting 5 V output with the INA126, you need a positive supply voltage of at least 5.9 V, and to be sure of getting a 0 V output you need a negative supply voltage below -0.95 V. If your load currents are very low, you may get away with smaller margins between the output voltages and the supply voltages.