I agree! We have three boys (now ages pre-school to pre-teen) and we've been taking them to Disney since our oldest was 18 months old. One thing we love about Disney is the fact that we don't have to rent a car. A few thoughts:
1) If you cab to Chef Mickey's and Crystal Palace (and assuming those are both MK days for you) you could take the bus back. Our cab fare to CR was approximately $18 with tip, and about the same for our cab to Ohana at the Poly for breakfast. If you have park hoppers and you leave MK before Epcot closes, you can hop on the monorail and stroll through Epcot on your way back to BC. We do this often - especially when we have someone asleep in the stroller! It's not necessarily the fastest route, but we enjoy it and we don't have to fold up the stroller to get on the bus.
2) It's relatively easy to take the early bus to AK for Tusker House. We did this in February without a problem.
3) We've always used a lightweight and easy-to-fold stroller at Disney, so we haven't had any difficulty with the buses. As long as our stroller reclines and includes a basket and a canopy, our kids have been fine. Our most recent is a Maclaren quest and we love it.
4) You might really appreciate Magical express with an almost-two-year-old! We've used Magical Express many, many times. It has always been super easy for us and our kids love it. (How can you beat a Disney-themed bus with a movie about WDW?) And of course, it's free! We always walk past the car rental counters and think how happy we are to be walking onto a bus, getting luggage assistance, etc. instead of standing in line at the car rental counter, installing a car seat, figuring out directions, etc.
Location and easy transportation are two significant benefits of staying at BC! Hope you have a great trip!!