Andy,
Yes, you're correct. You only become "commercial" and require a driver's log when you hook up the trailer but to satisfy a DOT logs check you will have to log at least one day before and after each trip.
I believe you need to show duty status for at least 34 hours prior to beginning the trip, to show that you have reset your hours. So, if you leave before 10AM, you would need the previous two days.
Also, not sure why you would need to log the day AFTER driving? I have never heard that. Why would you?