If your girls truly want to see the campus, you should fly to Chicago on Thur. and make your way to South Bend. There are a myriad of things to do and see on a Friday at your leisure. If you arrive on Sat. AM, there is little to no time to do or see much of the plethora of special events, sites, experiences that make Notre Dame so memorable. You can go to the Eck visitors center and arrange a tour or see a video of things to do or see. The Eck is a few yards east of the Bookstore which is a must do that may take anywhere from 10 minutes to 2 hours plus. If you truly can spend the day on campus, that allows time to tailgate prior to the game. Also, if you have time (and the game should end by 4:30), I highly recommend taking the family to the South Dining Hall for dinner...like dining in Hogwarts.
As for a quick day trip for the game, you will miss so much that is special about ND. Being at the game is just a part of the ND experience on game day. Watching the band form and marching to the stadium along with a couple thousand families of kids, parents, and grandparents is also special. There is so much to do and see that if you can take the extra day, it will provide a lifetime of memories.
More than anything, meet and enjoy the people that serve the multitudes on gameday....ushers, vendors, servers, information providers, etc.....they are a huge part of what makes Notre Dame so special and make every fan feel welcome.