The User profile is a system's folder and its location is hard coded into the registry. Many system services and programs just blindly attempt to write to that location by design. So, changing the User profile location can be risky but it is possible. There are a great number of methods each with its own caveats.
One method is to use , the way I do it, is with Windows Explorer and right clicking each profile folder, and changing their location from the location tab. This only works on most of the profile folders, but not all. Like the appdata folder you mentioned in your post can't be moved this way. IMHO this is the safest way.
A second method is by copying the Default profile and Public profile folders to a new location and making a registry edit. This works best right after an install with a fresh profile. I have never tried this method, so I cannot vouch for the type of results you may encounter.
See this link for a how to Second Method
The third method I came across involves using file system level redirection and NTFS symbolic link. Also, I have never tried this method either.
See this link for a how to Third method
.Very interesting read.
If you want everything moved and you got a well developed profile you might want to look into this method. Simply backing up the profile and restoring to a new location will not work because the system still thinks that the profile folders are still in their default location and will try to wirte to them.
Hope this helps.