I wondered why they rented a car and drove and I guess the articles above state why. I would never do that in some of these countries and particularly late at night and for that long distance. While some may worry about taxis, at least the legitimate taxis from the hotels to the airport, as well as the shuttles, have jobs they are concerned about, would be accounted for, and are far more apt to be trustworthy. However, with a motel 100 miles from the airport, their options were very likely limited or quite expensive.
I do not like the conflicting articles in the beginning, with one saying they did not check out of their motel and another saying they did.
If this was not random, my guess would be someone at the motel tipped off a "buddy". Their last day, although such side trips are awesome, and a deal at $20 per head, they encountered someone else who realized they would be driving and were tourists with $$ as you have to have for any trip. It also could be someone who just looks for this opportunity with rental cars towards the airports late at night. Someone from the rental car company could have even tipped off a friend. It also could have occurred when they were out in town that night. If she was worried and talking about her concern of the drive all day, it could have easily been overheard as well. Finally, if they were driving a rental car while there, which they were, any number of people may have known that over the course of the days there. This in no way is meant at the couple, just theories on what happened. Your hotels generally in such destinations know your airport, the day you are leaving and the time of your flight. They also should be able to provide the checkout time.
I do not know what happened here and I hope they are found safe. It does not bode well. The Dominican Rep has become a population tourist destination but like so many, one needs to realize that safety you feel is inside the tourist areas and even then, it can be a thin veneer.
I hope they are found and answers come. Both have children and that is heartbreaking as well.
This is totally jmo.