Since you have all the options, and can't see banks "C" and "D", I would first of all load in the latest version of the Korg operating system for the Trinity. It is 3.1.1 and you can get in on the Korg site. You could also obtain it, I believe on the Yahoo Trinity users group. Follow the directions. BE CAREFUL!!!
I also think you'll need to re-initialize the PBS-TRI that gives you banks "C" and "D". I've had to do that at least once and certainly had to after the unit was installed. There should be a disc that comes with it to allow that. If not let me know. That should do the trick.
Also, patches from the Rack and the keyboard will transfer nicely back and forth. The only caveat to remember is that the Rack has more multisamples (32mb ROM vs keyboard's 24 stock ROM). Any rack patches that utilize the additional multisamples will produce no sound on the keyboard. All multisample names and numbers are the same otherwise. Basically, if you dump all keyboard patches into the rack they will sound the same. Same for the rack into the keyboard unless the patch uses the additional multisamples. I just got the rack this week and discovered that through a little help from the Trinity users group.
Keep me posted.
--OKJ