Welcome to the forum! You present an interesting challenge.
I agree with Mark, though, in that I can't think of a way to route everything through your receiver like that. The two HDMI outputs just mirror each other on the 626. There might be a way, but I'm not seeing it right now.
However, you could achieve your end goal without too much work, I think. I'm assuming that you want to play movies on the second TV using some source (e.g. blu-ray player, PS3) that you'd normally use on the primary TV, so you want that source routed through the receiver. If you aren't already using the "TV/CD" input, the audio part might be pretty easy for you - the video portion may require an HDMI splitter. Page 40 of the Onkyo manual explains how to play audio from an audio-only input while watching video from another input (TV/CD is audio only). So, if you have your movie source hooked up via HDMI (assigned to one of the Onkyo's inputs) and a digital audio connection (assigned to the Onkyo's TV/CD input), you could watch and listen to movies on your primary TV over the HDMI connection, but listen to movies on the TV/CD audio input when you want to have audio only for the second TV while watching video from a different HDMI input on your primary TV.
As for getting video to the second TV that is different than what's on your primary TV, and if you only want that for one source (that is playing movies), an HDMI splitter should work great. If your source already has two HDMI outputs, you won't need one, but most sources don't. I bought this
Sewell splitter, and it works great.
Just let me know if any of that wasn't clear, or if you have any other questions.