With a very small differential signal like this you cannot compromise on CMRR (common-mode-rejection-ratio), PSRR (power supply rejection ratio) and Voffs (input offset voltage). This is exactly the situation a precision instrumentation amp like the INA125 is designed for, most opamps will have way too much input offset and offset variability to have a hope here - you'll just end up amplifying the input offset voltage to saturation or have a highly temperature-sensitive output value.