Hi, Allison!
When you have kids of different ages, the "divide and conquer!" method can be quite successful to keep everyone happy! No worries, in a few years all the kids will be zipping around on all the wild attractions while you get to enjoy a cool beverage while waiting on a shady park bench!
You will find many attractions that will allow 4 guests to be seated together. The Magic Kingdom will probably have the most attractions for you to enjoy all seated together: it's a small world,
Walt Disney World Railroad, Many Adventures of Winnie the Pooh, and more. There will be a Cast Member at the front of the queue, so ask him/her about seating before entering the line so you know for sure the attraction can accommodate you. In other parks, you will also find seating for 4 as well as you can always enjoy shows such as
Disney Junior - Live on Stage at Disney's Hollywood Studios where it is group/theater style seating.
I suggest with having two darling 2 year olds that you have a double stroller. It will be handy to have them secure and also a place to carry around tote bags and jackets.
Strollers can be rented at Walt Disney World or feel free to bring your stroller from home.
Wishing you and your beautiful family a magical visit to Walt Disney World!
Cathy