We won't be taking a stroller for my DD who will be 2 1/2 on our next trip. She never uses a stroller now, so I don't see the point. (We took one on our last trip when she was 18 months and she basically never used it.) If she needs to rest, we will rest.
My personal opinion (and I know this is the minority) is that it is better to just take the parks more slowly. I'm sorta shocked at how long kids stay in strollers these days. We are expecting #2 in a couple of months and people keep asking us if we are going to buy a double stroller -- it never even occured to me. However, I was raised this way -- neither my brother nor I used a stroller past 2.
I felt the same way as you. I don't like pushing big kids in a stroller (though I don't care if others do as that doesn't affect me) and never wanted a double stroller. At home my daughter walked everywhere. Like I said in an earlier post, we live in DC so it's not an option for us to drive everywhere are there are no free parking lots. So we walk, use the metro, etc. The kids go to school a mile from our house and we walk there and back everyday and the majority of our friends do the same. It's very unusual to see a kid over 3yo in a stroller here in DC.
My kids were 2.5 years apart so I didn't buy a double stroller. I wore the baby in WDW at 3 months and my daughter (2.5yo) used the stroller when she needed a break. Then last summer, when my kids were 4yo and 22 months, I went to WDW with friends. Just moms and kids, no dads on the trip. I knew that my daughter would get tired from the long days in the heat, resting on her schedule, in addition to my son's and our friends, was not going to be possible. So I broke down and bought a double stroller. I hated pushing the 90 lbs or so that they weighed with the stroller, but my daughter walked a good bit so that helped. However, she fell asleep in that stroller every single day. Whether it was an afternoon nap or she was done for the evening, either way she got tired at some point each day and needed the break. If I had gone back to the hotel for her to rest, I'd have my son to contend with (as they rarely napped at the same time, he was much more predictable following closer to his nap schedule at home). And while she's sleeping in the room, what do I do with him? And vice versa, where would my daughter go while my son is napping?
And then there's the issue of what would happen in the parks if my son was using/napping in the stroller and my daughter needed a rest. I couldn't carry her on my own while pushing the stroller, not to mention how tired I would be by the end of the day having to carry a 40 lbs child around.
With just one kid, it's easier to not use a stroller once they can walk for longer periods, but with more than one it gets tricky. We're having #3 in January and I can imagine that when #3 is 3yo and my other 2 are 6.5yo and 9yo, they're not gonna take too highly too to taking a break everytime the 3yo tires out while they can keep going. If we keep the youngest in a stroller though, then we don't have to worry about that one falling behind the rest of the pack by lunchtime.
Another thing to consider, specifically in your case, is that while my daughter never used her strollerby the time my son was born, the moment we brought him home and placed him in that stroller she broke down. Started crying hysterically that it was her stroller, she wanted to use it, and did not want him in it. Now I could have fought that battle, told her she was a big girl now, didn't need the stroller, they're for babies, etc. But a 2yo has enough going on with the addition of a sibling so I didn't think that would be conducive at all.
It was never an issue, she walked and we rested when we needed to.
I agree with this. Our plan is to have all of our DS's walk - the oldest will have just turned 10 and the twins will have just turned 5 the day before our trip 
