Hello,
The pressure sensor produces a full scale differential voltage of 25mV between +Vout and -Vout. However, I assume these voltages are offset from "ground" by one half the supply voltage (presumably one half of 10 volts or thereabouts), but the data sheet is not entirely clear on this.
It is unclear much differential gain you provide in your analog processing, and what measures you take to reduce the offset, but your post suggests that you are processing the +Vout and -Vout signals separately. To convert the 25mV differential signal, and provide a span from 0 to 5 volts suitable for the A/D, a differential gain of 200 would be required. I suspect that this will require a suitably precise differential "instrumentation amplifier" to achieve. I don't think that the use of LM358 operational amplifiers, in an instrumentation amplifier configuration, would be adequate because their initial offset voltage is comparable with the signal level, and the variation of offset with change of temperature would be unacceptable.
If the differential amplifier approach is used, only a single A/D input to the MCU would be necessary.
Regards,
Mac