I would definitely prioritize Magic Kingdom over the other parks.
Arriving your first day around 10am @ MCO, I would plan to not get to the parks until after lunch.
Maybe take a bit of time to have everyone check-in and get settled before rushing off to your first park. Are the twins swimmers? Maybe a quick lunch by the pool for an hour or two before getting everyone ready to go to MK.
It looks like park hours are set until 6pm on that day. Since you do have Genie+, I would suggest you book a ride that you feel would really start the family off excited while in MK. Will you have access to the internet at 7am EST? Having a ride or two or three “stacked” for when you get to the parks would help with the overwhelming emotions and sensory input you will have on day one.
Maybe Dumbo, IASW, and PPF. Throw in some extra fun time for an ice cream (the sandwich of course ), or cotton candy. A ride on the Carousel would be a great addition as well. If the children recognize some of the classic movies an songs, maybe give Philharmagic a try.
Unless the little ones can handle loud bangs, you may want to skip the fireworks or bring earmuffs. You always have access to the fireworks from within your hotel room (and can control the volume).
I would give MK, HS, and AK each a day. I would only add EP if the parents want a day at F&W. IMO, I think EP is tailored to an older demographic. However, you can weigh that against them getting to ride FEA and the RAT.
Definitely add mid-day breaks for naps and rest time by the pool.
I would add a day off maybe after the 3rd park day. (11/11)
To optimize the days, definitely take advantage of the Genie+ you have purchased. You will have to get someone in the family to be the point person for scheduling everything. Make sure they are diligent at the 7am drop and the 2 hour rule.
Make sure you do a “test” with the characters and the little ones. Some take right away to the characters, and some are just plain scared of them. If they are OK with the characters, maybe get them an autograph book and see how many character signatures they can get.