Forgive me for getting into the teaching mode. This quote needs some annotation:
According to my father, an occasional long drive will help the engine oil circulate through the drive train, which will help keep parts lubricated and working better longer.
The drive train includes engine, transmission, drive axle(s) and hubs. Your engine oil stays in your engine, I hope.
The long drive helps keeping the engine clean internally. I agree with that. The detergents in the fuel can better clean the back side of the intake valves. That's where deposits tend to from.
The detergents in the oil have a chance to clean the piston rings which allows them to move about inside their grooves and thus form a better seal with the cylinder wall. That improves and evens out compression.
The one thing that really keeps the engine alive is changing oil and coolant with the correct stuff at the proper intervals. And changing the spark plugs every 50000-100000 miles with the correct ones.
When your wife drives 13 miles between cold starts the engine has enough time to make the detergents work effectively. It's the frequent cold starts that kill an engine: I drive 3 miles to work, and run little errands. My engine is much more likely to gunk up than yours. Therefore it benefits from a longer drive on the weekends.
So, roll on, don't worry. musicmanmu.