Question about voltage divider
In essence this is what your original circuit looks like:







simulate this circuit &ndash; Schematic created using CircuitLab
The arrows don't really mean anything, they are just a node from which voltage is measured.
And when you add the LEDs it looks like this:







simulate this circuit
The bottom LED is not lighting up because there is no voltage across it.
D1 is lighting up because there is a voltage across it, but D2 is just shorted. The voltage on both sides of it is the same, so no current will flow through D2. 

Usually, in a case like this, we also include a negative label, like this:







simulate this circuit
Which means we are measuring (or solving for) the voltage across R2. Sometimes this is just left to:







simulate this circuit

When you say you   


  break the connection from after R2 to Vin   


This is what I assume you mean:







simulate this circuit

In this case, there is a voltage across D2, so current will flow through it.  In this case, there will not be as much current flowing through D2 as there is through D1, because the current also has to flow through the potentiometer R2 to get to ground.

In this description, I am oversimplifying LEDs some, because if there isn't enough of a voltage across the LED in the forward direction (usually about 3v for LEDs), not enough current will flow for the LED to turn on. However, since you seem to be using potentiometers in this setup, you may be adjusting those for the LEDs to have enough of a forward bias to turn on.