The Polynesian will be much more convenient if you plan on taking a mid day break and nap.
I advise taking umbrella strollers for both children. the monorail will allow you roll on and roll off convenience at the Polynesian whereas at the Yacht Club you will be dependent on busses. You will have to fold the stroller and your tired / sleepy children may have to stand on the bus. (Even in the most magical place on earth, most adults on those busses won't give up a seat to a child or parent holding a child.)
Also, while the Yacht Club is convenient to EPCOT, it is still a 10 to 15 minute walk with little ones in tow from the International Gateway.
Have fun wherever you stay!