Linking Amazon Echo To Hughesnet (satellite Network) Wi-fi

So I dropped my landline carrier (Century Link) and thus my DSL and subscribed to a satellite internet service (HughesNet). It's much faster (from about 13mps to 45 mps) compared to the DSL, which hardly ever reached its max of 1.5mps. Out here in the county DSL and satellite are our only two choices. Unfortunately my Amazon Echo (Gen 1 I think) won't link to the satellite's wi-fi network. It will link to my desktop computer's wi-fi, but this just sets up a wi-fi link between the computer and the Echo. There is no internet link. To get an internet link I have to connect the desktop to the HughesNet modem's wi-fi and this drops the connection to the Echo. Apparently the computer can only have one wi-fi link at a time. With the DSL I had the desktop wired to the modem with a LAN cable. I'd do that with the satellite modem but the installer of the HughesNet equipment hooked it up using the old Dish Network coax wiring (we dropped satellite TV a long time ago). Unfortunately this meant putting the modem in our bedroom which is across the hall from my office and computer. It seemed like a good idea at the time. Meant no crawling around in the attic and poking holes in the ceiling looking for interior walls through 24 inches of insulation. However, now it means attaching a LAN cable from the desktop to the modem would be difficult at best, unless I want to staple it to the walls and run it across the carpet in the hall (this was nixed by she-who-must-be-obeyed). The only way I can connect the Echo to a wi-fi is through the Alexa app on the computer, and that only lets you attach it to the computer you are working through (and the results are as described in sentence 3 above).
So I called Amazon support... they took control of my computer and danced around in it for a while and told me that there was a way to do it, and that I had "foreign ip addresses" in my network and to clean them up and make it possible to make the connection they would have to charge me. That's when I bailed out.
Bottom line: How do I make the Echo connect to the internet through the satellite modem? AND how do I get rid of "foreign IP addresses" in my network? Or do I really need to?
Keith