Hi, Kim! Your kids sound like mine when they were that age. It was difficult to keep them in a stroller with so much action going on! Unfortunately, there aren't partial-day rental options for strollers, but see if you like this suggestion. I think you should bring a lightweight stroller for your 2-year-old since it will be easier to keep track of him/her in the crowds -- especially when you're arriving at a park. Plus, it's nice to have something to keep all the "extra's" for the family -- a snack bag, rain ponchos, water bottles, etc.
Then, when one child needs a break and the other needs to stretch, you can swap places. We found that this helps the little ones keep up with the adults and bigger kids in our family without getting completely undone by lunch. Once you've figured out your family's "rhythm" in the parks -- early risers or night owls -- then, you can decide if an additional rented stroller is right for you. I hope this helps you plan!
Have a wonderful day and a magical vacation!