When you attempt to copy a disk, you should see some options to set the "Copy From" source, and the "Copy To" disk.

If you are not setting that, that would explain why it wants to use the one drive for both functions.

If you do not have an option to change either option to your second drive, then perhaps you did not connect the new drive correctly. Even if it is connected correctly you may not realize that many new computers, using SATA interfaces (a half-inch wide data cable) require a setting change in the BIOS to enable the new device.