I have never personally had this problem, but to the best of my knowledge WordPress does not have the system to support multiple users managing widgets at the same time, at least not widgets in the same widget areas.
Is it a problem to just have one user at a time manage the widgets? I can’t really imagine that being a problem, as 99% of the time you set widgets once and don’t change them for extended periods of time.
If the site requires that widgets be frequently (more than once per day), then I would seriously consider improving the site infrastructure to NOT require this. Use posts, pages, or custom post types to hold the content and widgets to display the items.