How can I force Steam to install a DLC to a different drive?
No, you can't, because DLC is an add-on to the base game. In order for the game to know where the DLC is, it has to be installed to a predefined location, ie. the game's install folder. That's why Steam doesn't ask you where you want to install it.
If you want to install the DLC to a different drive, you can configure the drive as a game location, move the base game over, tell Steam where the new location is, and then download the DLC. That will solve the problem.