It might help to know a little more about what you are trying to accomplish. Are both windows open at the same time on a single user's screen? Or is one window available to one user and the second being viewed by a separate user waiting to see the updates?
By themselves, the datawindows won't retrieve automatically on updates to the underlying table. In fact, if you have configured the datawindows properly, the update rules should provide some concurrency protection and will not let the second dw update the same table after the first updates. DataWindow2 will sense there's been a change and will try to prevent clobbering the DataWindow1's changes. But again, this may not be an issue if in your context the second window is read-only.
You could have the first window finish its update then check for the existence of the second window and have it retrieve. Even better, use a non-visual business object as an intermediate handler (and also keep nasty cross-window communication code out of the GUI). When the first window's update is successful have it tell the business object it's done, and the object can then tell the second window to retrieve. But there would need to be more done if your second window is updateable.