If I understand your post correct (and please correct me if I'm wrong).....

You can't "share" web  parts across team  sites. You can create a web part  and install it in multiple web part pages. The web part itself is able to tunnel back to a single data source so that information  updated in the data source will update on all installations of the web part. But I don't know of a way - nor have I heard of a way - to write a web part, install it on multiple web part pages, then update the original web part and have that update of the web part itself replicate to all current installations of the web part.

Does this make sense?