Right click on the desktop.
Select Display Settings
Make sure you see both monitors. Make sure it's set to "Extend display"
At that point, you should be able to select each individual monitor and set the resolution for each. If you want to flip one to be portrait, you should be able to do that too. Change that on the orientation drop down and pick the 'portrait flipped' option.
You should be able to do exactly what you describe..
In my office, we have a 3 monitor setup and one of those is usually set to portrait.
It's all in that initial Display Settings mode.
Good luck!
Mitch