Just something to think about, and may or may not be applicable to your situation.
I replaced OEM power steering fluid in both my cars a few years ago. First was my Honda Ody which had a "stick" or slight catch when turning in one direction. New OEM fluid did not resolve, so I tried Prestone synthetic for Asian. Same result. I then tried Lucas "for ALL power steering systems." The steering completely smoothed out in a day or two, and the problem has not returned since. I then attacked my Cad which had a slight catch in both directions. I started with maxlife given that the car was about 9 y.o. at the time. Did nothing to fix the problem. I then switched to Lucas and the problem was gone in about a week, and has not returned since. I did have to replace the high pressure hose later due to a cut, but that was a different issue.
Now, I realize Lucas is a favorite target of nay-sayers around here, but I am sold on their PS fluid. And their interior cleaner is pretty darn good! Now, the Lucas fuel injector cleaner was less than impressive (the only one that seems to work in my cars is techron).
Edit: to the OP, as others have said, it's fine to leave some dye in the system. However, while you have it apart you might as well just flush the whole system with new fluid. Whether it needs a cleaner (e.g., srafoam trans tune) or not depends on your situation. If it does, it wouldn't hurt to add this beforehand.
