Your problem is that you're running the repo as a file-based client, not
as a proper server.
Run svnserve or mod_subversion inside apache and give that access to
your repository files. Then your client connect to the server to perform
all svn operations.
Obviously, you'll need to run both the Windows and the Linux version of
svnserve to make this happen using the same repo - and might give you
issues with line endings (ie the Ubuntu version of svnserve will not be
able to read files created by the Windows version) but I think you might be
able to jiggle settings and run the linux version under Windows which might
be able to handle the linux-line endings correctly. Maybe.
This will solve your problem with the url - that looks like a Windows
path and not a Linux one (ie the E: drive letter suggests this). You will
not be able to re-wire this path (that is stored in the .svn directory DB
for your working copy) safely.
However, the best answer is to run a little linux VM that contains your
repo and a svn server, and mount it on both Windows and Ubuntu.