C.
Hello,
I didn't read all the responses word for word but it sounds like you have a lot of good advice and ideas of your own.
We went in April with our 4 and 2 year old boys. We had a lot of fun.
I did get and use the Unoffical guide to Disney book and found it very helpful. It gave us a plan before we even got to the park. We didn't have to waste time decided what to do or where to go, we knew.
I would agree with other poster on shipping some stuff to your hotel - you can buy items online from Amazon and ship them there or just buy them wherever you normally do and pack and ship yourself.
The stroller on the buses can be difficult (we have a tandem double too) but remember probably 25% of the other passengers have stroller too it's not like your the only one, people are good about it. I would definitely recomend taking it and not renting the rentals are $30 a day for a double and you have to leave it at the park gate so that means going to the buses or parking lot without it and carrying all your gear and possible kids too.
We did take a break everyday midday for lunch nap and some playground or swim time, this was invaluable.
I would also suggest since you are going as a group deciding what your plan is - is this trip about the kids, are you planning to ride adult rides too, is it okay if the group seperates etc. Decide those things up front to make the day easier.
Good Luck and have a blast!