The VIP211z has a component output that should work with your older TV if it has a component input (red, white, yellow - like for a video game, etc.) You would need to run a component cable back to the bedroom. Another option would be to use a
component to RF adapter: run a composite cable from the VIP211z to the RF adapter and connect the output of the RF adapter to the coax cable that runs from the front to your rear TV. Then you just tune the rear TV to channel 3 or 4, depending on how you set up the adapter up front. There should be a switch for you to select channel 3 or 4 on the RF adapter.
You would have to make channel selections at the VIP211z. I used to point my remote down the hall from the bedroom, when I had such a setup. The other alternative is to get an IR remote repeater, so you can use a remote in the bedroom, which relays a signal to the repeater near the VIP211z, which then signals the satellite box for whatever you have requested on the remote (i.e., channel change, volume change, etc.).