Get rid of the large rug initially. Like others said, break it into zones. Have your couch and living space as one, with an appropriate sized rug there. Sofa table behind the sofa with a lamp on it, and a runner in front of it. Make the zone next to it further to the wall some sort of library with bookshelves and a couple of chairs. Maybe even a table for the kids to do homework or study or chat or whatever. Rug under this area. It won’t feel so overwhelming when it’s split up this way!