At MK, you can still utilize rope drop for Adventureland and Frontierland. BUT, it is still a rush at 9am. My cousin was there last week and she said she felt like she was in a mosh pit trying to get to BTMRR

With that many in your group, I would look at the rides in those two lands and see if there are any must-dos and rope drop those, or everyone rope drop those lands but go to your priorities first. (Meaning it may not be worth it to grandma in a
scooter to race to BTMRR, but it may be well worth it for mom, dad and 2 older kids to hurry over there for a short wait. Not splitting up all day, just managing expectations for each ride.) OR if they have no idea what to expect, Magic Carpets and Pirates would both have short waits and be something everyone could do.
Fantasyland would have fairly short waits at Carousel, Little, Mermaid, Teacups and Dumbo till 10:30 or so. Even the princess meet and greets there take a bit to really get a line. Using
DAS, if the eligible child would ride would be the best option for 7DMT.
Unfortunately, during the bulk of the day 11-4pm your best bet for short waits are going to be Philharmagic, Carousel of Progress, Country Bears, Laugh Floor etc. but for someone who has never seen them, they can be a fun experience. By 5pm or so, you could probably hit up the Speedway and Buzz with a shortish wait. I would save the other big rides for closer to the end of the night for the shortest lines or do them one night during fireworks.
For Epcot, I would tour the countries in the morning when it was cooler and less crowded and then hit up Future World in the evening, waiti times are nearly non existent. Unfortunately, if you want to ride Remy and Frozen without early entry, I think your best bet would be to just suck it up and get in line whenever is most convenient. (Using the DAS here would be advantageous! Half the kids get Remy, the other half get to do Frozen) Walking a huge group front and back to Epcot several times would make for someone getting cranky
At AK, I would enjoy the animals, Rafikki’s planet watch, and Lion king show in the morning and hit rides later in the evening. Realizing that safari closes earlier than the park, but the wait drops off drastically for it in the afternoon. Riding FOP at closing or using the DAS would be of great benefit.
At HS, with both of your days I think you could get everything in but you will have to be a little savvier! You could probably do MMRR and the two secondary rides in TSL if you were motivated at the normal rope drop one morning. You would still have a bit of a wait but maybe not too bad. Then fill the day with shows and a break and do Star Wars land late that evening. Your second day go to ToT and RnRC, saving slinky for the end of the night?
Just some suggestions but I think with the mindset that you don’t have to do everything and that the kids won’t know what they are missing on some things, you will be able to find a happy medium. As a previous poster mentioned, make sure you do one must-do for everyone! And for many people, just being in the parks is magical itself. I would try hard not to put everyone in a 60-120 min line just bc it’s Disney and “you have to try this” ride kind of thing. Have fun!