From my experience in Istanbul, it would be a problem with a stroller! You would certainly get plenty of exercise pushing the thing up and down the pavements and the hills. If I was honest I would not have taken my children to Istanbul at such a young age but then Istanbullus??manange. Perhaps a native should answer this one.

you can also try posting your question in this travel forum...

http://forum.virtualtourist.com/7/forum-3038-1-Travel-Turkey-1-forum.html?wosid=0t32T073TsoO9nBBXwblO0

i travelled instanbul with children around the same age. My 2 year old didn't mind walking but a small stroller would have helped. Having a big stroller is no good on the streets, buses, or taxis. If you have a small stroller with good wheels you can manage. My kids played in the parks around the city with the other kids from the neighborhood or fed the birds and they had a good time. Museums not a place for the kids but a boat ride or just watching the boats go by with tea was great for them.