Turn off DRL using turn signal
In order to turn off the P-channel MOSFET, you need to raise its gate all the way to the 12V supply rail. Your filter circuit is only bringing it to some intermediate voltage. You need additional transistors in order to accomplish that.

Instead, I would recommend turning a 555 into a retriggerable monostable, which will give a nice "snap action" in terms of turning off and on the DRLs. Something like the following.







simulate this circuit &ndash; Schematic created using CircuitLab

Adjust the time constant (1.1 &times; R1 &times; C1) so that it's slightly longer than the "off" time of the turn signal. The DRL will turn off as soon as the turn signal comes on, and the DRL will come back on one time constant after the last turn signal flash.

The diodes and R4 help make the circuit rugged enough for the automotive environment.