I also have three kids who are a bit older than yours. When my kids were about the ages of your kids, the one time we stayed at the resort on arrival night, my kids were so mad and grumpy that I'll never do it again. All they wanted to do was get going! The next trip we went to Epcot on arrival night. Soarin' was on refurb and TT was closed because it rained all night. All we did was eat dinner and ride M:S and SE, and they said it was the "best night ever," because anything is better than sitting around when you are at WDW!
Because of the time difference, they may have a hard time sleeping anyway. I say go to MK! Get unpacked, eat dinner at the resort, and head to MK for the fireworks and see how it goes. Then take it easy the next morning.
Epcot is easy to do as a later arrival. I'd plan FP there from 9-10, 10-11, and 11-12, making your tier 1 either FEA or TT. I'd make the first FP one that isn't very important, and plan to arrive right at 10 and hit the end of it, knowing if you miss it, who cares. Then use the 10-11 and use the 11 right at 10:55 before heading to WS. Personally, I'd do SE, then M:S, then TT, and if we didn't show up until noon to use our TT, that would be okay. Then I'd plan spend the afternoon in WS and do the other side of FW, including Soarin', in the evening.