It has been a while since we stayed at POLY but with young children, the monorail to Magic Kingdom is a perk. Plus, you can see the fireworks from the beach.
We stayed at the Beach Club resort this past winter and LOVED it. Pool was great (even though parts were under construction) and the atmosphere was great. There is a goofy character breakfast buffet right there.
Here’s my thought on the Yacht Club resort - which we went to first by accident - it seemed more “stuffy”, more adults, all very dressed up, when we arrived, no kids running around. May have been a special event going on, not sure. The Beach Club was relaxed, with kids running around in the lobby, which made it much better for us (since we too have kids that run around in the lobby :laugh:).
The walk to EPCOT is wonderful. But, not sure how much time you will spend there with your short trip and young family.
Can’t really go wrong with whatever you choose, they are all great, but preference would be either POLY or BEACH.