Hmmm.
I see a lot of people have looked at your post, but no one has taken a shot at it. Let me be the first then

. You say that you don't like to take your DS anywhere. I think that a lot of people with 2 year olds feel the same way

!
I also have a 2 year old child, one who is in mid-snit as I type. At 2 years of age it's their job to establish their independence. To run, to refuse to sit in a cart, to scream when they don't get their way. Believe me, I know

. It's a very frustrating time for parents and child. Plus, if you both work out of the home you only see your child during the "witching hours" between 4 pm and 6 pm when all 2 year olds lose it and melt into a little puddle of uncooperative protoplasm. Of course, that's exactly when you need to go shopping.
You have 3 choices. (1) You can cancel your trip and possibly lose $$ and a much needed vacation. You will still have to deal with your DS at home. (2) You can go to WDW and leave your DS with a relative. IMO, you would miss him a lot if you did. (3) You can go on your vacation and make the best of it knowing you DS's temperament and limitations.
I have a couple of suggestions. Have you looked into getting a child harness or a hand leash? It might be your salvation. You can let your DS run all he wants and you still have control over him. Get him used to it now so it's not a surprise later. Maybe someone who's used one can suggest a good method. Even though he may not want to ride in a stroller most of the time, bring one anyway. Once he gets tired, he'll ride. Also, include nap time, swim time and down time in your schedule.
BTW: As with all snits, my DD's snit is already over and she's playing happily.