Oh, I didn't think of that. Oops.
Well, a bit of digging around seems to show that you really can't have different scenes on one channel, but here's something I found:
No. Same channel means same scene. You can still send RFCs via private messages to players elsewhere, however.
Perhaps you could have one channel for the "controllers" and one channel for the actual game scene, link them up somehow (I don't know if you can retrieve a list of players on a different channel than yours, but even if you can't, there's probably a workaround for that), then send RFCs using "private messages" (I really have no idea what that means, still a TNet newbie), and have the actual game process the input as per the initial plan.