Hey C.-
Everyone has given some great advice, so I'll try not to repeat too much! I used to work for WDW so I have some tips that I like to share that I learned about during my time down there!
First, utilize the bus/monorail/boat transportation to get around. Don't waste your time trying to park at the parks, and it's a waste of money. Since you'll be staying on property it will be very easy for you to travel by bus! And,the buses run around the clock, for the most part, so you can travel all around at your leisure!
Second, you really don't have to take a stroller, unless you really want to. They have great stroller rentals and I always heard parents talk about how much they loved the rental strollers! You can bring your own though, but the service is available.
Third, at your resort, purchase the plastic, travel, drink cups. You pay one price and can refill as much as you want, at any resort that sells them. This was the case a few years ago, but you may want to double check when you check-in. It's a great investment for your time at WDW and you'll have souvenir cups to take home!
Fourth, try to take advantage of the early park openings. This is where you can get in to the parks early, especially when you're up anyway with little ones! This is another thing to check in to when you check in!
Fifth, don't try to do all of the parks in one day or even during your whole trip. Take your time! If you only have a fews days, I would recommend the Magic Kingdom for sure, and the Animal Kingdom. These two are the best for younger kids.
Ok, so that is all I can think of for now! If you're like to email me back directly, please do so. I love to talk Disney!!
Have a great Trip!