Wow. It is amazing what you can learn on this board. I never even thought about the fact that there were no strollers. I think that even if they were allowed, they would be fairly difficult to use. There is an elevator, but the stairs are much more convenient. Do you have a snuggly? When my boys were little, I used to keep one of them in a snuggly and put the other in the shopping cart. It would free up your hands and make things a little easier. (Assuming that your one year old is closer to 12 months than 24 months). Just a thought, but the noise level may be a bit of a problem too.
Good luck.
Rebecca