We haven't stayed at the Swan, but have stayed at the Dolphin a bunch of times and have always had good luck getting in early (by 11 or 11:30). If your flight lands at 11, you will need to get lunch as soon as you arrive, I'd think. If your younger one is a stroller napper, I'd suggest lunch at the Swan or on the Boardwalk as soon as you arrive, and then stroll over to WS and see some shows or just take a stroll, get some gelato or other snacks in Italy or France, and then Tangierine Cafe (or Pizza) for dinner, then head back to the hotel and get to bed early.
On our last stay at the Dolphin, we were up at 4:30am for a 6 or 7am flight. Our girls are 6 and 2. Got to the Dolphin around 10:30. Checked in, dropped our bags off and put them in the stroller to go to Epcot. They were so wired from the flight and excited to be at Disney, so they actually walked a good part of the way there. We did a Soarin FP, I think, and had lunch at the QS there. We got a room ready text while we were on Soarin, so we headed back to the room and had a nap. After nap, I think we headed back to WS for dinner at Akershus or something (can't remember!) and a few shows/rides.
Our kids love Epcot. Don't write it off because it doesn't have obvious "kiddie" rides or shows, or isn't heavily themed. There is a lot of space to run around, walk around, and it is much more relaxed than most of the other parks because it feels less crowded and people are mellower, not running from attraction to attraction.