I understand the cost issue for a large family, but he said "so that we don’t have to deal with flying", not "it's too expensive".
Also, SFO to JFK is as low as $640 round trip for a family of 5 on the right days, and $760 in gas at 25 MPG and $3.30/gal. Plus you're going to need several nights of lodging unless you want to spend 40 straight hours in a car packed with kids.
I see you edited your comment to change the destination to Nebraska to make your numbers look better. Round trip SFO to Omaha for a family of 5 can be had for $655 according to Google Flights, vs. $440 in gas at 25 MPG and $3.30/gal, but again you'll need at least two nights of lodging for the whole family, and on a trip that long you should also account for part of an oil change and tire change and other car maintenance expenses.