For resort to resort transportation, if you have a car then that is your best bet. With your handicap tag you will also get free valet parking(don't forget to tip though) at resort that offer it. When getting to parks in most cases it is also easy to drive, the MK being the excpetion. When going to MK it is best to take the bus from your resort to MK since the buses drop off at the MK entrance, driving requires you to park at the TTC then walk to the monorail or ferry boat to cross the Seven Seas Lagoon.
I'm sure you already know this, but if I don't mention it somebody will, you cannot park at a resort and then head to a park while leaving your car at the resort. Resort parking is limited to 3hours(most of the time but not always). Some people have been told by the valets not to worry about the time limit, since the valets are the ones reponsible for making sure they have enough spaces they will know if longer parking is a problem.