I assume this is a typo:
Basically it takes a command signal +/-10V or 4-20mA and delivers a current to a solenoid proportionately between 0 to about 1500mA"
I think you meant to say +/-5V OR 0 to 10V.
(both have 10V range but one goes negative and the other doesn't.)
** (because "+/-10V" is how engineers describe a signal**
with a range from -10V TO +10V (A SPAN OF 20V,NOT 10V)
"Refer the sketch below. The Pins AI0 & AI1 will need to measure a +/-10V signal and hence a 2:1 divider is deployed. Like wise AI2 and AI3 will need to either measure +/-10V signal [or] 4-20mA signal. Just so that I display the proper mA values, I use a digital input on the connected NANO module. On the table in my office all of this work fine.
But in the field when they are connected to a proportional valve amplifier things go wrong and the values are no longer proper. I see the display values drop some 2 volts and also drift.
Due to the external amplifier configuration its possible that the 5V Ground gets linked with AI1 and AI3. Could this be an issue ? (It won't work if they aren't 'linked' as you put it. However THEY ARE NOT LINKED
IN YOUR SCHEMATIC.
Also when using differential inputs is it OK to use potential dividers as I have shown? "
You need to be able to read -5V before you can
say you can read +/-5V.
It is easier if you can use 4-20mA instead of 0 to 10V.
In order to do that without using 4-20mA , you
have to shift the +/-5V to 0 to +10V, then you
can use your voltage divider. If I understand
your post correctly. If you can't use 4-20mA then you will have to SUM the +/-5V signal with +5V
to get 0 to 10V (not the sane as +/-5V because
0 to 10V NEVER goes negative. You can then use
/2 voltage dividers to convert 0 to 10V to 0 to +5V
which can be read differentially with the ADS1115.
Looking at your OP, it looks like all you are missing is a GND connection on FB- & E.
Connect those two to the arduino and ADS115 GND
and it should work if the signal really is 0 to 10V and NOT +/-5V.
Is the relay for selecting 4-20mA mode ?