Tammy, first of all to solve the issue with quotes, you will need completely clear browser cache.
Concerning the topic issue, the main reason why I suggest you Amazon Storage as a solution is that you cannot storage images on another server because there is no existing file synchronization script. Even if you change URL for:
define('OW_URL_USERFILES', OW_URL_HOME.'ow_userfiles/');
you cannot change this path in the same way:
define('OW_DIR_USERFILES',OW_DIR_ROOT.'ow_userfiles'.DS);
You will need to configure NFS (Network File System) and this is not part of our competence.

"You will need to configure NFS (Network File System) and this is not part of our competence."

NFS is not necessary is this case because Tammy has one dedicated server only for 2 domains so nothing has to be shared via network. If no config can be done in OW for this, than sharing 1 directory for 2 web applications on the same server can be done via sym. links as I explained before (Make sure that both domains are able to read/write in that directory).

Our system doesn't  intend to change these constants:

define('OW_DIR_USERFILES', OW_DIR_ROOT.'ow_userfiles'.DS);
define('OW_DIR_STATIC', OW_DIR_ROOT.'ow_static'.DS);
define('OW_URL_STATIC', OW_URL_HOME.'ow_static/');
define('OW_URL_USERFILES', OW_URL_HOME.'ow_userfiles/');
define('OW_DIR_PLUGINFILES', OW_DIR_ROOT.'ow_pluginfiles/');

 What’s more as I know, we are going to delete this lines in future.
So even if you change this line:

define('OW_URL_USERFILES', OW_URL_HOME.'ow_userfiles/');

this will have no effect because the system doesn't use this constant for the image storage process. You may see this in /ow_system_plugins/base/bol/avatar_service.php file in this line:

 $urlsList[$userId] = OW::getStorage()->getFileUrl($prefix . $userId . '_' . $avatars[$userId]->hash . '.jpg');

As I said before, the best solution is to use Storage Services like Amazon S3.