Hi op. I have two just turned 3 year olds that we have taken to WDW 6 times since they turned 18 months so I will offer some advice. We loved, loved, loved CBR. To me, it's pool is one of the best for toddlers due to the zero entry pool and the gated pirate ship area with water features and small slides. In my experiences, they do enforce the under 48" height limit in the play area which I think is wonderful. We stayed in April here and had such a good time at the pool that we returned in September just to use the pool (we were legal pool hopping,
DVC members staying on points). But CBR is the only moderate with full size beds which you said you do not want. I didn't love that part of the other parts of the resort more than made up for it.
I will disagree with a PP who recommended CSR. Mthat is probably the last resort I would recommend for someone looking for a good pool with a toddler. We stayed here in June and overall, we really liked this resort as well. The rooms are beautiful but not very Disney, more like a nicer holiday inn or Hampton inn. We loved the food options here but, the big turn off for us was the pool. It's deep, no zero entry, and the toddler play area IMO is downright pitiful. Basically a plain wading pool. The slide is one of the best on property but most likely, too much for your two year old. We would gladly stay here again on an adult only trip or if we had older children.
I would recommend for a moderate resort (if you rule out CBR) you pick either POR or POFQ. POR has a very nice pool for the younger crowd, POFQ isn't too bad either. POFQ is a much more compact resort if that is important. Both of these resorts have queen beds. We haven't stayed at POR with toddlers and only walked the grounds of FQ.
As for value resorts, they all have double beds unless you book a family suite. We have stayed at all of the values except AoA multiple times. We stayed at movies for our boys second birthday and two months later in music. For the toddler crowd, we loved movies. It's the most compact of the all stars, the most recently renovated of the values (except the brand new AoA), and what kid doesn't love the big movie icons. We have never had a noise problem at a value, at least no worse than any other level. We have heard our neighbors in the deluxe resorts and moderate resorts. For a kitchenette, you would need to upgrade to a suite at AoA or all star music, so usually a bit priced than a moderate room. We stayed in a suite at music and loved it.
Here's my two cents on bus transportation. You never know what you are going to get. We have been going 4-6 times a year since 2000. Sometimes it's good, sometimes not. We have stayed at the same resorts and had differing experiences. You will see people reviewing the same resort on these boards for the same time period. One had problems with the buses, others had a perfect experience. During our stay at CSR this past June, I would say that was the best service we had. Short waits, always had a seat, no problems. But had I been staying in a different area of the resort I likely would have had a different opinion. We were the first stop. By the time we got to the third bus stop, we were standing room only, and the fourth, several times we drove by and picked nobody up and the driver called for another bus.
Hope this helps some. Ask any questions you need and happy planning!