I have such a wall splitter in front of my SB-HD and my single tuner DVR. I found (from reading another thread in this forum) that l could only get the internal tuner in the SB-HD to properly find the channels coming from that coax cable connected between the splitter and the SB-HD if I turned off power to the SB-HD, disconnect all cables to the SB-HD, then connected ONLY the coax cable from the splitter, then powered up the SB-HD and did a hard reset of the SB-HD, and setup the coax input only. Once I got that working, then power down the SB-HD again, connect the cables to the SB-HD from the DVR, power up the SB-HD, and then setup the second set of inputs (I think in my case it is using the S-Video connection for input) for the DVR source.
After I did that, everything works OK, and I can switch inputs being slung between the coax source and the S-video source. And each source has its own (and different) type of virtual remote displayed on the web browser (or standalone webplayer) screen on my computer.
It doesn't work that way with satellite; and in particular with DirecTV.
The 2 incomming coaxial connections are needed to be connected to sat 1 and sat 2 "in" on the back of the DVR. They are comming from the dish's LNB or a multiswitch.
DirecTV HD receivers as well as DirecTV HD DVR receivers only have 1 TV output although they contain multiple forms of output (composite, component, hdmi, etc). In your particular senario, you need another dedicated direcTV receiver hooked to the slingbox in order for it's exclusive use for the slingbox.
Dual tuner does NOT mean dual output in the case of DirecTV's gear.
You are going to need another, seperate, DirecTV source 'tuner' to do that. If you don't want another DVR (with it's attendent DVR lease fees), the way to go is what I've done:
Get one of the cheap receiver (non-DVR's) only for the second source. You'll pay the $5/month 'mirror' subscription fee, but nothing else, as you'll actual 'own' the box instead of 'leasing' it.. That's the setup I have in my living room, a HR20-700 DVR and a H20-100 receiver. I do have a couple other H20 DVR's, but they are scattered throughout the house (and one in my travel trailer during the summer months).
My big holdup right now is trying to get multiple component inputs with the Slingbox, that's a bit of a trick that so far eludes me, but maybe sometime in the future I can fee mr. Slingbox with multiple HD soucrces without having a carbon-based lifeform doing the actual switching at the box location. (!)