Found a solution.
The client machine can be accessed using \tsclient\\...
I first default the MyDocuments path in my application to Environment.SpecialFolder.MyDocuments which is of course the machine that the "server" of the remote app. Then I check for the existence and write access level of the following folders on the client machine
\\tsclient\C\Users\<username>\Documents
\\tsclient\C\Users\<domainname>.<username>\Documents
\\tsclient\D\Users\<username>\Documents
\\tsclient\D\Users\<domainname>.<username>\Documents
and then for XP...
\\tsclient\C\Documents and Settings\<username>\Documents
\\tsclient\D\Documents and Settings\<username>\Documents
If none of those exist then I use the folder on the "server" of the remote app.
Not the most elegant, but it works.