@Edward Fedorovich Another option to consider on the 1031 route is selling multiple properties and treating them as a single exchange and using the total proceeds to purchase replacement property/properties.

In return, they would theoretically agree to sell us the house when they're ready.Mom & sons continue to live there until they decide to sell (likely soon to pay for college) or until the divorce forces the sale.Once they are ready to sell, we buy it at a discount & flip it.Alternatively, maybe we buy out the husband's equity in exchange for part ownership in the property, then buy out the wife's portion when they are ready to move. 

This will include a GOOD hard money lender (or a few), an experienced Title person who knows the ins and outs of investor deals, and can offer investor discounts on title fees, a 1031 exchanger (the title person should have a good connection there), and a few contractors and/or subs for rehab work.

@Zocky Zhang, As everyone said, you can't exchange from investment property into your primary residence. 

Yesterday I did a Cash for Keys exchange, changed the locks, and took possession.Walking through the house, I’m trying to decide what to do with it.  

Although we had e-mail exchanges about his situation (he said he is trying and that he has some kind of job working from home), I have not officially sent him a 10-day notice but I am considering doing it this week.

If seller is in town then you can meet at tax collector office to do the exchange.

I believe they should do a 1031 exchange into a truly passive investment with monthly income.

You may not need to do a 1031 exchange.

As recently as Mar 23 I have a text exchange that goes something like this:Me after receiving update on her moving progress:  Ok will consider April as the last month as discussedTo which she responds: ok (then some more updates on moving)Then she's gone end of March, less than 30 days even, and I'm left with an empty unit for April.So if the new month comes before the 30 day period is up, does she legally owe all of April rent or only as much of April until that 30 day mark it hit?