This Slingbox doesn't have a built-in tuner so all it can do is transmit its input down the Internet for you to watch on your travels. But if you are using the same TV input to drive the Slingbox and to drive the TV then you have to both watch the same channel.
You need to give the Slingbox a different TV signal input to the one driving the TV, i.e. a second satellite box. Same logic as though you have bought a new TV for the bedroom, it needs it's own signal source.