There is this great blog by Jérémie Clabaut about hiding the "Open In Explorer" custom action…it however misses the a few points of what is trying to be accomplished by doing it.
Once you have deleted the section, end users can STILL access the explorer view via two methods:
1) The "Explorer View" via the dropdown on the right
2) "My Network Places" via windows explorer
In order to remove the the "Explorer View" on the library, you would need to delete it from the library settings page (at the bottom). BUT you would have to do this for every library that exists and every list that gets created! This means you would need to remove the view from the Site Definition for the document library so it doesn't get created every time.
For the second, there is nothing you can do but to remove the "Use Remote Interfaces – Use SOAP, Web DAV, or SharePoint Designer interfaces to access the Web site." permission from any Permission Level that the users are in! However, even though this SHOULD remove there ability to use Network Places, it does not (at least in pre-SP1 environment).
The last resort to prevent uploading of documents without entering metadata is to write an event handler that enforced those columns be there or you cancel their item add.
Chris