Seems like a lot of extra work. Just leave it in your car longer, ditto for her car.
You have two cars, A and B.
You put the oil in car A for 3000 miles, and then change it and run it in car B for 3000 miles. Putting a total of 6000 miles on that oil.
If you drive each car 12K miles/year, then you are doing 4 oil changes on each one of them, or 8 total oil changes/year. If we assume they each use 4 quarts of oil, then you are using a total of 16 quarts in your car, and then that same 16 quarts goes through the other car, 4 quarts at a time.
Now if you just changed the oil in your car every 6K miles, you would have two oil changes/year on each car for a total 4 oil changes, and use 8 quarts in your car.
Ditto for hers. Two oil changes per year on her car. Total oil useage is 16 quarts/year.
Seems like a lot of extra work for ZERO benefit. Even if you drive your car a lot more than she drives hers, just run the oil longer in your car, like 6K miles or even more.
Change hers at least annually, if not twice a year and be done with it.
But this seems to be a disaster in the making, not to mention a bunch of busy work.