We have stayed at the cabins and at CSR. We have not stayed at AofA.
We did not care for the cabins at all. We thought they were very inconvenient. We rented a golf cart (which cost more per day than our rental car!) and we still thought it was inconvenient to get from the cabin to the place where you get the boat to MK, etc. The pools are very boring. We did find the cabin itself pretty comfortable and the full kitchen was nice. But, if you want to eat out there are only two options -- take out pizza (they would not let us eat it in Crockett's Tavern) and the buffet. Our boys were 5 at the time and paying for a buffet for them for any meal (breakfast, lunch or dinner) made no sense. We decided that staying off-site would be more convenient than staying at the cabins. (ETA: I note that a PP indicates there is a themed pool at the cabins. Our stay was several years ago so if there is a themed pool, that is an improvement in that regard.)
As for CSR, we really enjoyed our stay there. The pool is themed and fun, the rooms are fine and we were able to park our car near our room. We took the car everywhere and found CSR to be centrally located to everything -- easy to get to Epcot, MK, DHS and AK. We weren't crazy about the eating choices, but at least one could go to the Pepper Market and get a variety of things without having to pay for a buffet for a child who eats almost nothing.
You might consider the All Star Music or AofA Family Suites instead of the cabins. They seem more convenient to me since you can park near your room and don't need to take internal buses around the resort or rent a golf cart. They will sleep 6 plus a toddler under 3 in two rooms (queen bed in one room, pull out sleeper sofa and chairs in the other room, and a pak n play), two TVs plus a small kitchenette area. I would do this rather than a cabin.