IF RB can handle two remotes at once, then consider this setup: your main remote operates RB as usual... let's say it's a Wiimote controlling a media center Mac. It operates over bluetooth, doesn't need a receiver, and works well at relatively close range (~15 feet, encompassing the distance from TV to couch).

Then you set up, say, a Keyspan RF FrontRow remote as the secondary one. It operates at long range, so if the tiBook is less than 60 feet away from the media Mac, you can use it right there. In the Sharing panel of System Preferences of the tiBook, do three things: 
1) change the 'computer name' to something simple like "wallbook". 
2) enable Apple Remote Desktop 
3) enable Remote Apple Events

The first two steps enable you to access the tiBook by pointing a free VNC client (like Chicken of the VNC) on another computer to "wallbook.local". The third step means that the tiBook is now Applescriptable, so to speak. You can run Applescripts on another machine on the network, and they will make things happen on the tiBook. Why? Now you can tell RB on the media Mac to assign Applescripts to the buttons of the Keyspan RF remote, and you can write those applescripts in such a way that they operate on the tiBook in the other room.

Obviously there are some caveats: you can only assign two scripts to each button on the remote, so your control over the tiBook is kind of limited. But if it's just meant to be a digital picture frame, and if you write sophisticated scripts, maybe that's okay. Also, as stated above, this would only work if RB supports two different remotes with separate functions for their respective buttons. I don't know if that's true or not.

If RB can't handle two remotes at once, you have another option: cut RB out of the process for purposes of the tiBook. If you can find a Keyspan DMR, its software allows you to assign Applescripts to its buttons directly, so you can approximate the above functionality without RB, and just use RB for the media Mac. The caveat here is that the Keyspan DMR is no longer sold... I don't know if its replacements, the iTunes remote and the Express remote, use the same software (I know the RF remote does NOT). If they do, then they would work as well.

Finally, FYI, you can find tiBook hinge replacement kits on Ebay for about $100, much less than professional replacement. You have to be comfortable with partially taking the machine apart and using high-grade glue or bonding stuff to put the new hinges in, but I did it a few years ago and it has breathed new life into my tiBook. I had to re-glue the new hinges once but they are otherwise workign great.