There are good suggestions here. We tend to pair MK with EP because of being able to take the monorail between these 2 parks. Anywhere but between MK and EP you can take a bus from park to park. I'm not sure it always saves time vs. taking a bus between parks, but at the very least, we like riding the monorail a few times per trip, something that we associate with being at WDW. And with that, I would go to EP in the am to rope drop the 3 main attractions, round out the other few Future World attractions, walk around World Showcase, eat lunch, then head to MK in the afternoon. While rope drop is more effective at MK with its many attractions in close proximity (esp. Fri am with EMH - early), with only 2 park days... I'd want to finish at MK so you can experience Happily Ever After fireworks. You can allocate more time towards MK though by leaving EP right after lunch or earlier in the afternoon since there is a lot more to do at MK.
Hence on Thurs., I'd try rope drop AK which would have EMH early and finish at HS. And if you're not going after Flight of Passage because of your kids there'd be less pressure to show up the standard 1.5 hrs before AK opening, which happens to be 7am with EMH for your stay. That's pretty early. You could either start at river journey first or Safari with minimal waiting. You'd have to plan the shows (Nemo, Lion King, and the bird show) in order to get to them early enough to leave for HS at a decent time and probably have to skip some of the AK/HS shows.
When we were taking just Sat single day trips, we always went to either AK or HS first followed by EP in the afternoon, monorail to MK at night... and got to all of the main attractions. But we also don't have kids yet and run everywhere. We once ran into a guy who was trying to be 7th person, at the time, to hit all of the WDW rides (excluding shows) in 1 day. He was rope dropping Slinky Dog on an early HS day and I think he was finishing at MK.