That is exactly how I play - gameclient on my 24-inch external monitor and anything else on the laptop.
Fullscreen never worked right for a separate monitor - ever. I used a Scotthope autohotkey file for correcting the sizing after opening - until recently when WGT made some change.
A hint - if you get it set up the way you want - dont touch the video options again. I decided to try something different and it took me quite some time to get it to show properly again!