Is there a SVN software that'd allow to work with a remote copy? So far I've checked cornerstone and versionapp, neither of which allows to do that.

I've also tried mounting a remote disk (SFTP) using Transmit 2, but that resulted in an error when I've tried to checkout the SVN or add a working copy later on.
This may be a silly to suggest, but Nautilus on Ubuntu Linux has mounting of network drives, and ssh repositories and such built it very nicely. I used to edit code using this method with gedit. As for the mac, I would say that Transmit with its MacFUSE plugin is probably what I would use. What error are you getting?