I'm not a satellite guy, so I will be no help with your set up. But I can ask clarifying questions with the best of them!
Have you tried what you are asking about? It may or may not work, but no harm in trying.
Hooking up satellite is one of the most frustrating things our members try to do. There are a lot of variables in the hookups. Satellite will not go through a regular splitter and must use special splitters designed for satellite use. That's one variable.
I'd suggest listing your model and year, setting it up as you suggested, and draw out a diagram of it. If it works, great. If not post it (the diagram) and see what kind of responses you get to try. You have to start somewhere. Hope this helps a little.