changing the directory on motion should not cause a change on the web server. Was it working before you change the directory?
If not, then look for webcam_localhost and control_localhost config option.
If yes, then I suspect permission problem. I had to change the permission to 666 to enable read/write by everyone.
If you run it as service, then the user name isn't "pi". username is "motion", group "motion". At least, that's how it's set up on my device.
Raspberry Pi Journal: http://simpletongeek.blogspot.com/p/raspberry-pi-journal-directory_4.html