Even though your receiver says SWM that just means this option is available but does not require it. The picture shows only 1 coax so I am guessing the ANTENNA has the SWM hardware making it usable by the receiver. When you move it to the RV you can add the SWM8 hardware as mentioned above and still require the 1 coax coming into the RV to watch and record 2 different (SD) channels. You will also need to change a couple of settings in the receiver to show SD channels only and you may have to change the antenna type setting.
If you don't want to go SWM the current receiver will work with the older technology but does require the 2nd coax to be run from the dome to the receiver.