How to wire a relay for 12v car lighting
Power a relay from the switched headlight power.  Then put the NC (normally closed) contact in series with the daytime lights.  When the relay is unpowered, the daytime lights work normally.  When the relay is energized, the NC contact opens, and turns off the daytime lights.

Any "12 V" relay that can handle whatever the current of the daytime lights are is good enough.  Make sure to look at the relay's DC current rating.  That is usually lower than the AC current rating.

Since you are driving a relay coil directly with no other electronics, you don't need to worry about the voltage spikes on the car power line.  Relay coils aren't going to be damaged by the occasional spike.