I have cruised several times and 9 times on Disney and I am telling you right now that is an amazing and very affordable vacation compared to a land package at Disney World. Add in how much it would cost for room service, soda, all your meals and the fact that you get to go to out of the country destinations and your not even required to have a passport, a cruise wins hands down in my book.
I lurk this forum due to hubbies type 1 diabetes for tips and tricks from others here. So, I don't normally post here and I don't have a family member in a wheelchair. However, I do know someone that rented a
scooter and had it delivered to the Disney Dream and they had a great experience with all of it. They let Guest Services keep the scooter for them as it was too tight in the cabin. However, if you request a back of the ship cabin I have seen them out in the hall. I wouldn't do it, but their is a little indent on some decks that you can park it behind.
That being said, I have to agree with the DisneyKidsDad that said you should request an accessible stateroom if it will make onboard life easier for you. They are limited to how many they have on each ship so don't hesitate on requesting one, do it ASAP. You can book DCL up to two years in advance and people do, so availability can get very limited for these stateroom types very fast.
One of the benefits of the accessible staterooms is the larger balconies, the extra space in the rooms themselves so you won't feel as crowded and the roll in shower.
Their are elevators so getting around the ship will be easy and the only port I can think of that has a tender that most ships sail too is Grand Cayman. Otherwise, it won't be fun but their is a kind of a steep solid floor ramp to get on and off the ship. So you can roll on and off.
You can't ask for a better crew, they will be so accommodating for you and assist you with any needs you may have including dining. The only downside to sailing DCL, is that you will compare everything back to this and DCL is really hard to beat. The only thing I have found that can come close is Royal Caribbean.
But, don't take my words for it! Check out the DCL forum here, their are folks that have cruised DCL way more than I have with all kinds of different needs and the fellow boarders are always happy to answer questions just like here.
Unique to DCL...Door decorations and FE's.
Enjoy and happy sailings!