Business & farm

This does get tricky as there are many different positions that can be taken, however, I am inclined to side with CPA#1 and this is why:  

I am referencing this article, which states:

To deduct expenses for business travel within the U.S., the trip must be "entirely" business-related. If you had some incidental personal travel within the trip - visiting family or taking a side trip, for example - the expenses relating to the personal activities (gas miles to someone's home or hotel at a personal location) are not deductible business expenses.

If the trip is primarily personal, like a vacation, you cannot deduct business expenses unless you can show that these expenses are directly related to your business. For example, if you take a vacation and spend a morning visiting a client, you can deduct the cost of the visit, but not the cost of getting from your tax home to the client's location.

I think your scenario matches the second paragraph - the primary purpose of the travel was personal, so you can only deduct the mileage from Lincoln to Kearney and back to Lincoln.

This is also true of what is in IRS Pub 463 (https://www.irs.gov/publications/p463#en_US_2019_publink100033803) if you click on Travel in the United States, Trip Primarily for Personal Reason:

If your trip was primarily for personal reasons, such as a vacation, the entire cost of the trip is a nondeductible personal expense. However, you can deduct any expenses you have while at your destination that are directly related to your business.

A trip to a resort or on a cruise ship may be a vacation even if the promoter advertises that it is primarily for business. The scheduling of incidental business activities during a trip, such as viewing videotapes or attending lectures dealing with general subjects, won’t change what is really a vacation into a business trip.

The IRS Pub is pretty clear that only the expense related to business can be deducted (mileage from Lincoln to Kearney and back).