Hi, Tricia!
Wow! Triplets! That has got to keep mommy super busy!
From the Polynesian, you can take a monorail directly to the Magic Kingdom, and you can walk to the Transportation and Ticket Center where you can take a monorail directly to Epcot. Buses are available to Animal Kingdom and Hollywood Studios.
At the Beach Club, you can walk to Epcot, take a boat to Hollywood Studios, and buses are available to Animal Kingdom and Magic Kingdom.
You will have to decide what is best for your family, but I would lean toward the Polynesian. I think transportation might be easier, and I think your kids will like the Volcano Pool and Captain Cooks food court. There is even a great
Kids Club if mom and dad want a night out! There are many nice restaurants to choose from, and a quiet walk on the beach might be nice.
Whatever you decide, have a great time in Walt Disney World!