Welcome to the Community !
Its really easy to prove/disprove:
#0: Prerequisite: Remove your router during the troubleshooting phase by connecting a single computer directly to the Hughes Modem.
#1: Get a screenshot of your "fuel gauge" just before shutdown and note the time: (I like this one):
#2: Disconnect the LAN cable from the rear of the Hughes Modem: (the one next to the red arrow)
Leave off for whatever period of time suits your schedule
#3: Startup: Reconnect the modems LAN cable
#4: Note the time and immediately take another screenshot of your "fuel gage":
#5: Post the "before & after" fuel gauge screenshots along with the shutdown/startup times and the Mods will do the rest.
Intercepting the results:
If, under the above conditions (that is ... modem is isolated) you had usage .. then the problem is on the Hughes end.
If, under the above conditions, no usage occurred then the usage is likely the result of something on your network and there are tools and procedures to find out just where the problem is.