Lots of great advice above. For the record, our experience --
We rented a car and used it exclusively. (I have a couple health issues that make me more comfortable with having my own vehicle on hand.)
Epcot, AK, HS, all very easy with the car.
I got a lot of advice about not taking the car to MK because of just what described above -- you have to park at the Transportation Center and then still take either the monorail or the ferry to Magic Kingdom itself. But we took the car anyhow, and I ended up being glad we did because I LOVE LOVE LOVE the ferry. There's just something magical, for me, about floating up to the park on it, and floating away at night. It's a bit of a walk from the parking, but for me that was fine. The ferry never had a wait (other than waiting for the ferry to pull up, it might be on the other side of the lake or on its way) and it's huge, and I found it a fun and now-essential part of my MK visits. I'm not sure which solution would be best for you in your circumstances, but for the record it can be an enjoyable way to get there.