Hi Lauren,
Thank you for visiting the Disney Parks Moms Panel with your question. It's a tough one ... all three Disney Resort Hotels are absolutely beautiful and unique in their own way. If I had to choose, I'd suggest
Disney's Polynesian Resort for your family. With two little ones in strollers, the ease of the monorail will become the best amenity of your vacation. When staying at a monorail resort, there typically is no need to break down the stroller at the end of each evening when visiting Epcot or Magic Kingdom. This becomes a lifesaver with two sleepy toddlers, and I imagine you'll spend hours upon hours in the Magic Kingdom during your stay!
Dining options are plentiful, ambience is tropical and relaxing, and proximity to both the Ticket and Transportation Center and the monorail makes traveling a breeze. With small children, you'll love the beach and zero depth entry into the popular Nanea Volcano Pool. Can you tell I love the Poly?
What other questions can I answer for you, Lauren? You really wouldn't go wrong choosing any of the three resorts, but I especially think you'd love the amenities and location catering to your family's needs at Disney's Polynesian. I hope my answer was helpful and please feel free to visit me again with any follow up questions.
Sherri