I don't claim to be an expert on all this and have not done it myself, but.........
Have you installed both monitors' drivers?
If yes, it's time to go into the Catalyst Control Centre and try and configure 2nd monitor. I would look very carefully at the CCC help files and google the topic. It all made sense with the old CCC; I recently tried with the new one and got lost. I only downloaded the new one in an attempt to fix a problem. It was terminal, and I'm on nVidia now
Having seen PC's set up for screen and laptop with quite different properties, I'm sure it can be done!