Add another relay, so the 12V output of the foglight relay activates it (as well as powering the foglights). Use the NC (normally closed) contacts as a switch in line with the supply voltage from the battery, maybe between the existing DRL relay and the DRL lamps themselves. When the foglights are on, it activates the new relay, opens the NC contacts, and the DRL's go off.
If you want that behavior to be optional, put a switch in the wire between the 12V foglight relay output, and the new relay.
Relays can be powerful friends.
Spott