Controlling a relay with a MCU output pin and trying to drive a solenoid using the same power source
You shouldn't be driving your relay from 12V_Protect, but directly from a voltage source that doesn't have the direct possibility to "leech current" from C16.

Approach: 

    Schottky
 12V --&gt;|------+-------&gt;|--- &gt;to C16
      D0       |       D1
          12V_Protect


A sufficiently sized Schottky diode will have lower voltage drop even when the relay draws a lot of current. D1 isn't strictly necessary afterwards, but would mitigate the "my relay draws so much current that my stabilizing capacitor gets discharged" problem.

Then: measure 12V_Protect across the coil when you directly connect the coil between 12V_Protect and ground.

If it's much smaller than the nominal voltage of your power supply: your supply is too weak and can't supply enough current. Get a better 12V supply, or a relay that needs less current.