I agree with the majority that while it won't be an easy day it's totally doable and worth it for 3 extra weeks in your home country.
I agree with booking 3 plus 1 seats if it's a 3/3 plane lay out so you can block in the younger 2 and have 11 year old across aisle next to you. If it's a 2 4 2 layout then I would take middle 4 with you and 11 yo on the outside to block.
If you have an ADHD diagnosis or DLA letter you can ask the airline to apply DPNA code to your booking (if his condition is severe enough to mean he cannot comply with normal instructions safely etc) and you can also present yourselves at the special assistance desk at the airport on arrival at the check in (this doesn't need pre booked and is separate to the airline code) . They are always very helpful and will escort you through fast track to the gate, cutting down queues and extra help and understanding at security which is the hardest part.
The other crunch point solo with kids is boarding. If possibly don't fly with a budget airline - but as you say it's 4 hours I guess it could be. Just be aware that they use the worst gates and often the bus transfer to and from plane which my worst experiences of flying with young/SEN kids. Just be prepared for it not to be fun. I've found longer flights short haul with more distractions like meals and entertainment panel far easier than 3-4 hours short no-frills flights. Fully charged tablet/device for each child with headphones is essential IMO - sharing will just cause extra conflict.
Eldest is well old enough for you to spell it out to them that they can have 3 more weeks holiday with family but only if they can step up and be the second grown up for you on the flight no matter how annoying their siblings get. Otherwise you all have to leave with Dad. Bribery is a great idea here too.
Agree with minimal luggage. Backpack each x 4 is plenty and not having a wheelie makes life easier, check in just 1/2 big cases that the oldest can pull.
With a 4 yo I would still be inclined to take a buggy and get it tagged to take to gate which helps in departures if you have delays and they are tired. But be aware they often don't return them at gate and you can have a long walk to arrivals. So minimal luggage means if you have to carry them older 2 can take all the bags.
Like others I've only done it with 2 but one of mine has significant additional needs. Had to do it regularly as we also lived a few hours flight from home country. Won't lie I've had some awful flights but it was always worth it for the time with family. Does ADHD child have ear defenders? They can really help when it's all a bit overwhelming.
Unless you are hundreds of miles from an airport in UK then book a transfer to collect you. They aren't that expensive when you take into account the cost of trains for all of you. I use this platform as they book and confirm for you using local firms. The driver meets you with a sign at arrivals and helps with luggage.
https://city-airport-taxis.com/ in recent years I've found the driver usually texts or WhatsApps you before the flight departs to check.
Good luck. It will be fine, and honestly even if it's not a fun day, you will get home and it's more than worth it to get those 3 weeks.