Are you talking about a rental stroller or a rental car? I assume rental stroller based on the prior responses. I would think long and hard about renting a stroller. We have never done it, but we love our stroller and even use it when we walk to the bus stops or the monorail platforms. But using the stroller outside of the park is only a minor consideration. Just research the rentals to make sure they work for you. If you meant a rental car, always take Disney transportation - especially MK. Our very first trip we tested driving v. Disney transpo and we found the car very useful for DTD and other resort dining, but not for the parks.
FYI, we are former monorail resort or bust type WDW guests who finally decided to purchase DVC (wanted the kitchenette). We stayed recently at VWL (with DD5 and infant) and barely missed the monorail. Yes, we loved being able to walk to MK from CR and then be the first stop back on the monorail. And yes, the MK views are amazing. But unless you only do MK and Epcot, you will have to utilize the buses at some point.
Getting on the bus can be a small pain, but it is really not that big of a deal.
We can't wait to try our "home" resort at BCV in September - walking to Epcot and boating to MGM. If you prefer the Epcot resort area, then I would just do that. Since you will have young children, you may want to consider getting a studio - it was so nice with the baby. Of course, with the Epcot resorts or the monorail resorts, you really can't go wrong.