I do not think you have to necessarily stretch, but it helps to start hiking slowly, and then do a "cool down" at the end of the day. Once you have camp set up, moving around often helps. As for driving home, I stop a lot and walk around. I really do this more to stay awake!

I do not get stiff unless I exceed what I normally do. Occasionally I will hike 20-25 miles out the last day, camp at the trailhead, and then I AM stiff in the morning! That said, as a tradition, I purposely do a 3-5 day killer backpack early season and suffer greatly. I probably should tone that down as I get older.