Yeah, the SQLDMO libraries are pretty fussy about where it'll back up to - mapped drives can cause problems and going out of domain will definitely not work.
fortunately, the hard working folks in the FMS planned for this - diRT (be sure to get the latest from www.CiscoUnityTools.com) has an option called "two hop" backup. It does the backup locally and then copies the backup to the remote destination (either a UNC or mapped drive) and then deletes the local copy. so you can setup a scheduled backup and have it work OK in this fashion.