2 years ago we took our double jogger (it's a mountain buggy urban double) for our then almost 1 year old DD and DS2.5. It was great to have in the parks, we stayed off-site and had our own car, so getting to the parks was fine (there were no busses to deal with).
Our only real problem was using the tram from the parking lot at MK. It wasn't too bad when we arrived, but leaving was hard. It was DH, DSIL and I with the 2 sleeping kids that DSIL and I held while poor DH had to fold up the stroller and try to get it on the tram by himself. These really nice teenagers tried to help us and the other people on the tram were really nice, but it was a struggle.
As far as the monorail - we took the ferry over instead. You can just roll right onto that, so no problems.
Last year when we went, we took 2 umbrellas because we did not want to deal with the big double.
This year, we are taking a jeep double umbrella stroller. It folds up very easily and is easier to carry folded up. DS is going to want to walk a lot, which means DD will attempt to too and we did not want to have to push 2 empty strollers.
It sounds like you already have another stroller to bring, so 2 singles probably wouldn't work (unless I misread your post).
Bottom line, it is not impossible, people do it all the time and I am sure you'll be fine. But, if you have the opportunity/ability to take 2 singles or a smaller double instead, I would do that.
Have a great trip whatever you decide!
