With the 622 you have 2 tuners and 2 TV outputs. Don't confuse them. You can run from the TV1 outputs to a "nearby" TV with composite, component, or HDMI cables. TV1 is HD or SD. You can also run to TV2 in a remote location by either composite or coax, and it's SD only; HD sources will be downconverted. In your case it sounds like the coax cable to the 3rd room is the answer. Connect that coax to the "agile" modulated output of the 622 and either the off-air or cable RF input on the TV in that remote 3rd room. The 622 can then be programmed to output one or two modulated TV signals for TV2 on that cable. If you use the off-air input of that 3rd TV then you can set the 622 to modulate onto two channels between 21 and 69 - choose ones that don't overlap any other signals on that cable. (TV2 can also operate on CATV channels 73 to 125.) Then you would need to tune your 3rd TV to receive those 2 channels.
What you transfer from the 622 depends on which mode to which you have it set. In the "Single" mode both tuners in the 622 are available to TV1 in order to use the PIP feature, but you can also receive that same signal (including PIP) at the remote TV on the TV1 channel (the "Shared" feature must be enabled). Both remote controls can control that combined tuner function. When the 622 is in the "Dual" mode, then each tuner is independent. Tuner 1 is controled by the IR (green) remote control at the TV1 location and tuner 2 is controlled by the RF (blue) remote at the TV2 location. Both are completely independent in the dual mode. You can receive the tuner 1 and tuner 2 signals on whatever channels you assigned them to, but the green remote controls only tuner 1 and the blue remote only tuner 2. Check your owner's manual for the recording and playback operation in the 2 modes.
In your case it sounds like you should find a way to connect that coax cable to the 3rd room to the RF output of the 622 in order to use the tuners and remotes like I described above.
(I received my 622 only a week ago so I haven't had a chance to explore all it's features and capabilities. I think what I stated above is correct, but I might have missed something, so YMMV...!)
