2 miles is a fairly leisurely 35 minute walk. Just enough time to really contemplate something about work or life, without getting bored and tired. Good exercise too; you'd be walking enough each day to make a difference. And even in the harshest cold, you wouldn't freeze, as long as you're properly dressed.
If you do that and after a couple months you see the car just sitting... and sitting... and sitting there, you might do well to sell it and not replace it with anything. You will really have to calculate its total costs as it sits there. Depreciation has pretty much already finished, so now it's just maintenance, taxes, insurance, fees, yada yada, and the occasional gas. If you end up needing a car for 20 miles a month, you'd hardly notice the difference between a 12mpg car and a 120mpg car. But if you end up needing it for 20 miles a month, you might do well to just use whatever your wife drives.
You might eventually sell both and buy one car, for your wife to drive daily, with a good mileage rating and a decently large capacity. There are actually plenty of SUVs out there that are built on a sedan base, not a truck base, which get around 30MPG, plus or minus a few miles. Then you can walk to work, your wife drives, and you occasionally borrow the car to do construction-y things.