My son (18 months) religiously takes a 3 hour nap at 10 am. Much to my dismay, he started to give up afternoon naps when he was about your son's age, although every once in a while he'll go back to it. Make sure that your nap routine is an abbreviated version of your bedtime routine (same music, same books, same lovey, etc.) and make it consistent. And as for the afternoon nap, at his age you might not be able to force sleep. Some babies have given up that 2nd nap by then. But you can encourage "quiet time" - at the same time each afternoon, do the nap routine and then put him down with a book or a soft, quiet toy. Turn off the lights, tell him "you don't have to sleep but you have to rest" and say you'll be back in an hour (or whatever). Of course if he screams, maybe that won't work. But if he can play quietly and maybe even fall alseep from it, then great! It's worth a try.
I read Dr. Weissbluth's book, too, and it helped us. Our son is a champion sleeper. However, many posters said to make your son's one nap be the afternoon one but if that's not his style, then let him sleep in the morning. Although it's "normal" for toddlers to nap in the afternoon, some (like mine and his cousin) prefer the morning. If I had to force him to stay awake until 1 pm, we'd both be miserable! About a month ago, I did push his morning nap back about a half-hour and he started to nap longer, so that may help. Plus, the morning nap suits our lifestyle. I like not being tied to the house all afternoon.
My other strategy for that time in the afternoon where he won't sleep, but is obviously too tired for play, is to just go out for a walk. Take advantage of this great weather. Your son might fall asleep in the stroller, or at the very least the fresh air will energize you both. Listen to some music, stop to get a coffee, or go to a forest preserve. I LOVE taking walks - it's the only way I know to take a "break" while my son is still with me!
Good luck and enjoy your summer - I taught before my son was born and I know how liberated you feel!