UPDATE: FAILED SIMPLIFIED SETUP. REVISED.

Unfailed: Understanding/explanation of original fail, at the bottom.

Simplified Setup:

   5V
   ^
   |
   |    
  _|_   +
 /   \ 
| Vs  | V_Source (to Measure)
 \___/
   |    -
   |
   |    +
   \
R2 /   V_R2 
   \
   |    -
   v
  GND

We want to measure V_Source, with an oscilloscope. So, attach Channel 1 to V_Source+, attach Channel 2 to V_Source-

  Vin
   ^
   |
V1 *---------------> 'Scope Ch1
  _|_   +
 /   \ 
| Vs  | V_Source (to Measure)
 \___/
   |    -
V2 *---------------> 'Scope Ch2
   |
   |    
   \
R2 /    
   \
   |    
   v
  GND

Set your 'scope to "Add[itive]" Mode. Set Channel 2 to "Inverted."

Then you get a single trace on the scope which shows:

V_Trace = V1 - V2 = V_Source

Excellent!

------------------------------------------------------

Set both 'scope channels to 0.5Volts/Division.

V_Trace appears to be AC: 0.1V

Trace (V/Div = 0.5V):
---|------------------------|---- 1.0V
   |                        |
---|------------------------|---- 0.5V
   | _   _   _   _   _   _  |
---|/ \_/ \_/ \_/ \_/ \_/ \_|---- 0V
   |                        |
---|------------------------|---- -0.5V
   |                        |
---|------------------------|---- -1.0V

EXCELLENT!

------------------------------------------------------

Adjust 'scope channels to 50mV/Division.

(Leave everything else the same)

V_Trace appears to be AC: 0.01V

Trace (V/Div = 0.05V):
---|------------------------|---- 0.10V
   |                        |
---|------------------------|---- 0.05V
   | _   _   _   _   _   _  |
---|/ \_/ \_/ \_/ \_/ \_/ \_|---- 0V
   |                        |
---|------------------------|---- -0.05V
   |                        |
---|------------------------|---- -0.10V

WTF????????

WAS EXPECTING:

Trace (V/Div = 0.05V): 
(Image zoomed in Time/Div, 
 but NOT V/Div, 
 for ASCII Art)
---|----__----------------_|---- 0.10V
   |   /  \              / |
---|--/----\------------/--|---- 0.05V
   | /      \          /   |
---|/--------\--------/----|---- 0V
   |          \      /     |
---|-----------\----/------|---- -0.05V
   |            \__/       |
---|-----------------------|---- -0.10V

Again... V_Source was already measured to be 0.1V in the 500mV/Div setting, but now appears to be 0.01V in the 50mV/Div setting. W T F.

That was *measured on the same 'scope* just seconds prior...

So why are we seeing V_Source=0.01V when we saw 0.1V before?!

-----------------------------------------

Think about it, verify your connections, check for broken solder-joints, swear at the universe, etc. for an hour like I did... (Remember, I simplified this experience for yah; my circuit's a bit more complex... and I didn't just switch the 'scope's knobs, I also switched to a duplicate, but not identical, circuit inbetween steps... which resulted in checking the new circuit is right *over and over*).

Finally:

Adjust those 'scope signals to make sure you saw what you saw at 0.5V/Div...

Whoa, wait... it is the same as it was last time! Yep, we are in fact seeing the same signal appear as 0.01V when viewed at 50mV/Div, and 0.1V when viewed at 0.5V/Div... Something's wrong with the 'scope? I don't use 50mV/Div very often...

----------------------------------------

Didja figure it out yet....?

-----------------------------------------

Spoiler Alert!

-----------------------------------------

Here's a hint...

Vin = DC: 5V

The 'scope's set to 50mV/division...

The scope *shows* 10 divisions, that's 500mV total shown on the screen...

The two channels are set in Subtractive-mode...

So, we have one 'scope channel at something like 5VDC + 0.05VAC... and the other at something like 5V - 0.05VAC.

The 5V offset-voltage is feeding into the two probes...

But is unseen in the trace due to being in subtractive mode.

The 50mV/Div setting means that we're amplifying that 5V offset, on each probe, and likely hitting the amplifiers' rails. Duh