This is a major problem with the UI design at the moment. By making the UI area "split", they forced us to constantly switch between views and try to manage information in a very non-intuitive way.
Additionally, the same thing happens if you're trying to compare an item in a listing to your inventory vs your companion's equipped items. There's no way to keep a vendor open while checking both your inventory and your companion screen, so you have to either write down the stats or remember them while you look around.
I believe that if they fix the "only two windows open at one time" issue, most of these problems will go away.
Movable windows would be a nice touch, too.