There's not a perfect solution for your specific question/situation. You can't tell iTunes to use a different backup folder, especially one that isn't always connected to the laptop.
One thing you can do is to find the backup subfolder containing your phone's backup (located in %AppData%\Apple Computer\MobileSync\Backup) and manually move it to your external drive. If you ever wanted to restore it you'd have to manually copy it back. It is going to be named with a cryptic number, but you'll be able to figure out which one it is based on its size (right click on the folder and view its properties).
That's not a long term solution though. Bottom line is if you want to regularly back up your phone you're going to need a computer with more local storage on it. I also wonder why your backup is so huge, but that gets into an entirely different discussion.