When my various weather radar sources couldn't answer my questions with the precision that I wanted, I found a new iOS app that could.
Dark Sky ($3.99 in Apple's App Store) matches weather radar with the exact location of my iPhone or iPad to estimate, almost to the minute, when rain or snow will arrive, when it will peak, and when it will stop. The app also has a highly-detailed radar image that pinpoints any active storms across the country and displays them in a way-cool blue-on-black map.
Dark Sky told me that, although the sky above my head was indeed quite dark, it wouldn't actually start delivering rain for another 40 minutes. Its shimmering graph indicated that the rainfall would be light and that the drizzle would let up in about 90 minutes. The prediction was spot on, pleasing both me and the dog.