What I understand, is that you would like to stream one channel while the TV is playing a different one.
I can see what you're doing with the splitters, but let me ask you. Did you try to put the splitter before the Cable Box and the Slingbox?
For example coaxial cable coming from the wall > splitter > 1 end to the Slingbox and 1 end to the Cable Box.
That way, you should be able to resolve that problem.