HD-DVD and Blu-Ray have DRM issues. To be fair so does DVD, but it seems the MPAA has mostly given up on that front...
You can use the remote to control MythTV and its plugins, including MythDVD. One thing to note, however, is that the Myth Transcode Daemon does not get started by default. You can just start it manually rather easily though. The program name is mtd. Just typing mtd in a terminal will get it going. I just added mtd to /etc/rc.local and had /etc/init.d/rc.local start at run level 2. That way it's always running.