If I want to configure settings and open ports, I need to log in to the router, but can't, because no one knows the admin name, and it's apparently unrecoverable. If I reset the router, would I just have to go to adapter settings on the other computers and put in the new settings, or is there more? How difficult might it be to reset a router and set it up to connect to two adapters?

Download all the updates for the version of router you have.
Then wipe the old install, and reboot.
Now you can start over with a new install of the router... once you have it properly installed, everything should be fine.

You only need reset the router (do you know how? - usually there's a recessed button you need depress for a few seconds.. often you need a paper clip to access the reset button) This will set it back to factory settigns

then just reconfigure it (download the user manual from the mfr web site if you need it)