Hughesnet is currently the only option for me as an ISP, but their modem/router is pretty limited talking about functionality. The build-in Wifi antennas do not cover the whole area in our home. I would like to use a router with OpenWRT and the Hughesnet modem only for the satellite communication. Where should I start. Any recommendation is very much appreciated. Thanks a lot in advance!
Take a look at the Hardware Questions and Recommendations section of the forums and/or the OpenWrt Table of Hardware to find a router that is supported by OpenWrt and meets your needs.
While you are doing this evaluation, consider that you may be best off using a main router + one or more dumb APs strategically placed around your home. Wired ethernet will give you the best performance, but if your situation doesn't allow for wires, there are other options including WDS and mesh (wireless uplink methods), but you'll want to make sure the hardware you choose works well with these methods.