A Lesson and Question Regarding "Resizing Hot Linked Images"

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While I don't consider myself and expert in Drupal, I do host around 50 drupal web sites on my Fedora Core10 server and I've been able to figure out nearly all aspects of Drupal and php by using this Forum and existing posts. However, I'm having a heck of a time wrapping my brain around the ability to resize hotlinked images.

For example. I have a site http://lonestarfishing.necomputerservice.com . Members are using photobucket and other hosting places to post images, then hotlinking them to posts within lonestarfishing.necomputerservice.com (no www ). When posted, these images are enormous and break the spirit of the theme. For example, see here http://lonestarfishing.necomputerservice.com/?q=node/1 . Is it even possible to resize images that aren't hosted on the Drupal site? I have to make this baby-friendly as the users are not computer literate nor do they understand how to resize the images themselves prior to posting on photobucket.

So I've been reading the Drupal Forums and it looks like the solution is not easy. I've tried several modules and scripts but nothing works correctly. Can someone that has the skills in this area give me a push in the right direction?

Thanks in advance.