Hi Molly, and welcome to planDisney!
You have come to the right place, and to be honest, because you are already thinking of ways to vacation at
Walt Disney World Resort, you have already begun the process, congratulations!
Vacationing on a budget is the best way to go. I would start by determining when you would like to visit. This is important because there is a difference between traveling in February and December. After all, December has been known to be a bit pricier. Once you pinpoint when you want to visit, next is the resort. The best resorts that could fit your family's needs would be resorts like
Disney's All-Star Movies Resort or
Disney's Pop Century Resort. After you decide where you will stay, you need to think about your theme park tickets. I do not believe it is necessary to visit all four theme parks in one visit, especially with the ages of your little ones. I recommend choosing two theme parks, such as Magic Kingdom Park and Disney's Animal Kingdom Theme Park. You can always plan another visit to experience the other theme parks when your babies are older.
I think that a four-night stay would be a great start. You can visit the theme parks for two days, enjoy your resort amenities, pools, and even spend some time at Disney Springs. In addition, you can always save money purchasing your water, snacks, or quick breakfast items from one of the local retail stores.
Please come back if you have any more questions. We want to help you through this process.
Have a magical time!
Raquel