I´ll try to show a better picture:
supply voltage for the circuit is 12V and GND
one device gives an outupt of 2 to 10V
another device wants it´s input starting with 0V, max 10V (or 12V)
I want to connect this two devices
A 2V reference is available
Unless it's mandatory that you scale the external circuitry to the arduino 0-5vdc range for maximum steps of resolution, just use appropriate sized passive voltage dividers such that the maximum possible external measurement signal equals 5vdc, then use specific software map() functions for each different analog input pin.
The first channel can use a resistor divider (/2), giving a 1-5vdc measurement range so the map function could be map(channel1_reading, 205,1023, 0, myMaxUnits#1);
The second channel if indeed 0-10vdc max, use also a /2 divider for that signal giving 0-5vdc input, and map(channel2_reading,0,1023,0,myMaxUnits#2).
That should at least let you move on with the project. You can always come back and design and build external hardware op-amp to scale and offset that channel1 voltage if it's really required, but it's probably really not needed.