I will not count the driving from home to the library to the gym as a local trip. Here's why - there is a leg of the trip that is well over 3 miles - 4 miles, to be exact - from the library to the gym. So, it's not really a local trip.
Now, if I were to go back home after dropping Davan off at the library, that part of the trip would be local and would have to be counted as such. I'd already decided, however, that if I make a local stop on the way to a non-local place, it didn't count as a local trip.
Justifying? Maybe. But, I still think I'm staying in the spirit of my resolution and I feel comfortable with the decision. Besides, so far the tally is 23.5 bike/walk to 3.5 car. That's not too shabby, me thinks.