By default, when the RUTX11 connected successfully on a WiFi AP (e.g. your satellite modem), regardless if you are connected via LAN port of WiFi too, you should have a internet connectivity too.
My guess is that either the RUTX11 is not authenticated in the satellite modem WiFi AP or there might be a conflict with the IP address.
Can you send a screenshot of your configs, LAN IP of the RUTX11, and the WAN IP once it is connected to the satellite WiFi AP. - Network → WAN.