I'm not sure how keen you'll be to this recommendation, but what about a backpack/ back carrier for you and carry your 2 year old??? Like I said, I'm not sure how heavy he is, but with weight baring exercise, you can do less and get more benefit than just pushing the stroller. He may enjoy the experience a little more and you'll definitely get more out of it. It may not be an option, but I actually did this with my son for a LONG time (until he was about 25lbs) and only when I got pregnant with my second did I stop. It got me into GREAT shape, aerobically and anaerobically, and it was just walking so that got me so excited!
The only other option is make sure that you strap him in TIGHTLY so he can't stand up and just endure the "looks" for walking with a screaming child! Either way, don't give up on YOU! Your exercise and sanity are JUST as important as your childrens welfare and happiness.
Good Luck--R.