I, like you, HATE carrying things around while in the parks. I got a Canon Rebel XT a few years ago for Christmas and took it to
Disneyland just over a year ago. I took a small jansport backpack (mini size) to carry it and found it a HUGE pain to take in and out of my bag. In fact, there was one entire day where I never took it out because we met up with friends for the day and I didn't want to be a pest!
I also took it in an over-the-shoulder bag (the overland donner bag) to EAA airventure last summer. I started feeling faint and dizzy from carrying all the weight between that and water bottles etc. From that point on I decided if I bring it, I'm just going to carry it straight out and bring a ziploc to put it in for water rides...if I bring it at all.
For that reason, while I absolutely LOVE my DSLR, I'm strongly considering one of those teeny weenie Sony digital cameras to take to the parks from now on. It will fit in a pocket and I won't have to worry with lenses, tons of batteries, huge bags, etc. I just am over the carrying huge bags everywhere thing.
Yes. It's going to cost me more money, but for the photo quality, I don't find it worth it at this point. I'm not trying to step on toes, but it seems that so far, the people posting replies are the ones who don't really mind carrying bags or have a stroller to put them in. I'm in the same boat as you-I really like to carry as little as possible. I don't even carry a purse!!
If you can't get a second camera (maybe with wedding money?), I'd suggest seeing if you could borrow one from a friend or if all else fails, bring one lens and carry it around your neck with no bag so you can stick it in wife's purse for rides and such in a ziploc or something. They're sturdier than they seem. I've dropped mine a couple times (not on purpose, of course) and it's always been fine. Changing lenses is too much of a pain unless you're there for 2 weeks and have all the time in the world to set up perfect shots everywhere you go.