Hi Beth,
I believe the cabins are located in the 2100 to 2800 loops. From any of these loops, you should be able walk to a bus stop is 5 minutes or less. As welovemickey stated, if you are planning to spend a lot of time in the campground, you may have to hop on the buses if you don't have a cart. On our last trip, we had a cabin near the entrance of the 2100 loop. Just to give you an idea of walking time, we were less than a minute to the bus stop and about 5 minutes to the Meadow Trading Post. On serveral occasions, we would return to FW on buses that dropped everyone off at the Pioneer Hall area and then left FW again. Rather than wait for an internal bus and load the kids and strollers again, we would walk back to our cabin (loop 2100). This walk was about 15 minutes.
If you can get a cabin in the 2100-2300 loops, you don't mind walking a bit, and you have a stroller for your 2 yo, I would think you could get by easy enough without the golf cart (assuming your parents are ok with walking also). It is only a 5-10 minutes walk to the Meadow Trading Post, Bike Barn, Campfire, and Pool area and you can always take a bus to the Pioneer Hall/Petting Farm/Marina area if you need to.
If you are in the 2700-2800 area, I would think your only two options are a cart or the buses (unless you have bikes). It is a long walk from there to get to anything
If you haven't already done so, you can request a particluar loop on your reservation. We have stayed in many of the cabin loops and we like 2100 the best. It is also very close to the comfort station in loop 1100, so if you need to do laundry while you are there, it is close by.
Our kids really enjoyed walking around FW... they were as interested spotting animals and birds along the trail as they were in getting to our destination. With your 3 kids ranging in age between 2 and 8, FW is the best place to stay, it has the most things to do, and your kids will love it.