You have now provided (barely) a schematic, so I will try to answer the question. However, this schematic is still a mess. Remember that a schematic is for communicating a circuit, not some busywork we assign that you have to do to check off some item. Ditch the stupid fritzing software if that's what's causing these messes, although I suspect it is probably possible to make understandable schematics with it. Unfortunately the temptation will still be there to create those really annoying wiring diagrams, so it's still probably best to use some other software that forces you to think about the schematic only.
In any case, here are the things I see wrong with your circuits:
- The power is never connected to the processor. In the top schematic, there are only two leads going to it. One is (apparently) ground, and the other is (presumably) a PWM output. The processor won't run like that.
- The "-" pin of the 12 V power plug is connected to the processor, but its function is not labeled. This looks like it's intended to be ground, but we can't tell.
- There is no current limiting resistor in series with the LED. If the processor were properly powered and the gate driven high enough, the LED would be quickly destroyed, depending on the current capablity of the 12 V supply.
- You mention pots in your description, but show none in either schematic. We therefore can't tell what you are tweaking and what effects it might have on the circuit.
- The schematic would be a lot more readable if it followed proper practises. In particular, power at top, ground at bottom, and logical flow left to right would help a great deal. As it is now, I have to stand on my head to decipher the schematic instead of just looking at it to see the circuit.
These various circuit errors and inconsistancies make it impossible to talk about these circuits further. Remember that we are volunteers here, so minimizing hassle of and showing some respect to those you seek a favor from is in your own best interest.
You have now supplied a more readable schematic. Things are a lot clearer now, but this also brings up a new question. You say these LEDs are "12 V". There is no such thing as a LED that works on anywhere near 12 V. You could have some kind of lamp assembly that includes the LED and a resistor or maybe some kind of power supply, but your schematic shows bare LEDs, so this is confusing. It matters because if you really have bare LEDs then you need the current limiting resistors. If you have a integrated unit that requires 12 V to operate correctly, then you need to not have the current limiting resistors.
In any case, it makes no sense that one LED should come on dimly when the other is driven. This could be caused by a bad ground connection between the FETs and the processor. Drive one LED on and the other off, and check the gate voltage of the FET that is supposed to be off. Check it right at the fet, and also from the gate back to the ground at the processor. It should be a few mV at most in both cases. Also check what the drain voltages are of the FETs when both are off, one is on, and both are on.