This may or may not work for you but it did for us. My DD was a little over 2 when we went to WDW the 1st time. She was not a stroller rider either, much preffered running or being carried! I made a big point of purchasing a new slimmer stroller for her, she shopped with me- sat in it and helped pick it out, we talked about how she would need to ride in it at Disney. We talked about it regularly in the weeks before the trip. Once we got there we talked about how tomorrow she would ride in the stroller and go see Mickey and the other charecters---basically really talked it up but always saying she would ride in the stroller.
The first day we were going to the parks we left the hotel room and as it was quite a ways from the bus stop we made that our 'testing zone'. We told her she needed to get in and ride so we could go see Disney. She, not unexpectedly, had a tantrum about it and wanted to be carried. We just stood and waited talking encouragely about the things that were going to happen once she got in her stroller and we could get to Disney. It took maybe 15 minutes (although it seemed forever) and she got it out of her system and realized that we meant business and she got in and away we went. We had maybe a minor fuss once or twice later in the trip but I think we had established that we were serious and she wasn't going to be carried or running free.
Like I said this may not work for every kid and DH and I had talked about it and really steeled ourselves for the tantrum and knew that we were not giving in--it was super important for us to be on the same page because he will often 'give in' when she fusses. We also prepared the older kids telling them it would take a while that first day but they were cool with it as they had been prepared.
Anyways it is a thought...just sharing my experience.