Yes, the boats are all handicap accessible. All of the Epcot hotels are great! The YC/BC share a large swimming area called Storm Along Bay (SAB). SAB is beautiful and it winds around a lot with bridges and foliage. As a result, there are no places where you can easily watch children play without possibly losing sight of them. Some people with younger children find this to be a problem. There are two 'quiet' pools which are plain and rectangular that can be used here as well. The BC has a nice, family friendly beach atmosphere, the quick service restaurant, Cape May Cafe (the character buffet( and is the closest to Epcot. The YC is a bit more subdued, is closest to the boat dock and is the first bus stop pick up. The BC rooms may have a full balcony or may have a standing room only balcony. Almost all the UC rooms have a balcony.
The BWI is a lot of fun. There are a lot of activities going on at the BW itself in the evening. This resort feels a bit closer to DHS to me, but is also very close to Epcot. Room balcony sizes do vary somewhat but I believe that most have enough room to sit upon. The BWI has a very nice quiet pool area and a themed area that has a clown face that has the water slide. Some people (myself included) find the clown creepy. If you don't then you may find this pool area better for younger children for swimming. It is probably easier to keep track of them here.
For walking to/from the Swan/Dolphin everyday I would pick the BWI. It is just across the bridge from these resorts. The YC/BC aren't far but they are further away for walking.
The Swan/Dolphin are great hotels, but a large part of their charm i the price. If you aren't paying the tab, I would stay in one of the other three. If Club Level is available, I would definitely choose the BWI. The CL there is the best in the area, Hands down! If not choose the theme that you prefer and consider the pool situation for your children. All three resorts are awesome! With a split stay tab the CR, you will have the best vacation!!!
Enjoy!