Personally, I'd definitely rent one for the 4 year old at the very least. I've used Kingdom Strollers many times and have had exceptional service. They even refund your money if you end up deciding before the trip that you don't want the stroller afterall. And they include a free rain cover and cooler to be used with the stroller. For me, I'd rather have it and not need it than have an exhausted and cranky 4 year old! Not mention, a stroller makes a very convenient way to carry souvenirs, purses and drinks!
Hope this helps! Have a great trip!