There is nothing in WordPress that would prevent you from dragging more than one instance of any widget into a sidebar. So, if this is happening on your admin panel under Appearance > Widgets, it means there is some error with something, maybe a third-party plugin that adds a widget’s options form incorrectly, maybe a browser issue.
Putting that aside, the default WordPress categories widget will not allow you to show anything but simply all categories, anyway. So, that’s not what you want. I would suggest searching around wordpress.org for some plugin you can experiment with like this one: http://wordpress.org/extend/plugins/extended-categories-widget/
Search all plugins: http://wordpress.org/extend/plugins/