If I understand your question correctly, you have the cable from the SWM antenna connected to the power inserter - this provides the power that the SWM LNBs and their multiplexor require.
The output from the power inserter then goes to the televisions. I think it likely that your distribution center box acts as a splitter to route the signal from the antenna through the power inserter, and then to either none, one, or both of your TVs.
The probable issue is that to support the multiplexing of signals on the SWM cable, any splitter in the system must work over a broad signal band (typically specified at 2 to 2150 MHz). It's possible that your distribution center supports this bandwidth, or perhaps not.
The easiest thing to do is to try using both TVs through the dist. center selecting channels from multiple satellites. If it works, you are good. If it doesn't then you'll have to consider adding splitters and signal source selection switches in addition to your distribution center.
