There are plenty of HDMI splitters (more technically, distribution amps), the trick is finding one that works properly in such a setup. Most current ones seem to create their own EDID, and report back the "lowest common denominator" of the capabilities of the downstream connected devices. You could end up telling the devices upstream of the splitter that you can only handle 2 channel audio (from the TV's EDID and only 2d video (from the AVRs EDID). Search this forum for Scubawoman's post... she seems to have found a splitter that works well for her, and she has similar equipment to you (and me). However, another consideration is, if your DHC 9.9 is similar to my Onkyo 875 (and I expect it probably is), you probably experience some audio and video delay going through the AVR due to the internal processing it does. If you delay the audio, but send the video straight to your TV, you may end up with lip sync issues. Another thing to consider: you won't lose lossless audio if you do toslink from the DirecTV receiver to the AVR, since plain old Dolby Digital is the best you can get out of DirecTV. But that still doesn't solve the lip sync issue, and also doesn't help you if you're trying to use the AVR as a switcher to allow multiple devices like the PS3 to connect to the adapter.
You are essentially in the same boat I and others are. Neither DirecTV nor Mitsubishi really thought things out (or just didn't care enough) about how their components would work with other components in a typical home theater setup. We are trying to petition DirecTV to modify their current software to allow us to enable 3d output even if their receiver doesn't detect a 3d device directly connected to it. See this thread, and this thread, but most importantly, post your setup in this thread, and explain why you need to go through your AVR.