Quick question for you: Are you using any software to control both toons or just alt tabbing between windows?

What I think is happening is that the one in the background is minimized meaning that your computer allocates a lot less resources to it. This would lead to lag (so the position of your second character on the fiurst screen isn't where the second character actually is) and also alt tabbing seems to break follow sometimes.

I'd suggest trying to run both in windowed mode, so you can have your main screen at the front, but your second screen won't actually be minimized (and so should get more resources going it's way).