It should work like you describe, assuming you have the proper setup. Different shows can be watched on each TV and the PVR works independently as well. When you set up a recorded event it should show you which TV (TV1 or TV2) it will record from and allow you to change that as well.
Do you have the receiver set up in dual mode? On the front of the box ensure the light is over the dual-mode icon, and if it isn't then change the mode.
Do you have the proper remotes? For the 2nd TV, your remote should have a large "2" at the bottom (in that semi-circle area that says "UHF" on the regular remote, it will show a big 2 and on ours it's colour-coded in blue vs. the black on the standard remote). If you're just using a regular remote that isn't coded to TV2, then it won't be changing the channels properly on the second signal.
If you have the above showing properly and it still isn't working, then I recommend you hire Paulo on this board to troubleshoot the setup for you. He hooked ours up originally, and he does excellent work:
http://www.hawthornevillager.com/phpbb/ ... hp?t=17457