I agree with considering a 1 bedroom villa at a DVC resort. Renting points may be cheaper for the room, but then do you miss out on all the European freebies like free dining, cheaper tickets, etc, I assume? If so, you can still book these villas with a cash reservation through Disney and get those freebies, cheaper tickets Etc. Those freebies may save you more by booking with cash than renting DVC points ( which also are not typically able to be cancelled or modified). The 1 bedroom gives you a king bed, two baths, queen sized sleeper sofa in living room and pull out twin sized chair bed in living room (at least in AKV Kidani and BLT, maybe others). You get a full kitchen and washer dryer. Less packing/checked bags due to having a washer/dryer can save in checked bag fees. We order groceries (and beer and wine and liquor) through
www.gardengrocer.com. They deliver right to resort, where Bell Services keeps all refrigerated until your room is ready. Minimum $40 order and delivery fee is $14. Delivery is $2 on over $200. Great service. We usually order all breakfast stuff (waste of time and money to eat breakfast at a restaurant for my kids, who just want cereal and fruit!), dinner stuff for several nights, water, snacks, soft drinks for room, sandwich stuff if we are in room at lunch. Can also order diapers Etc if you need that. You will not get a cab to the store and back, with tip, for less than $14, I don't think. And it's at your resort when you arrive. This saves us a TON of money on food, snacks, and drinks. But if you get free dining, you may just need it for breakfast, snacks and drinks. Still worth it to me. Order several weeks in advance on line to get choice of delivery times. They also give 10% off your order if placed 60 days in advance.
Secondly, couldn't agree more to add water parks to your tickets. So much fun, my kids want to do them more than the parks a lot of days! And doesn't use your parks days on tickets as I understand (we use military tickets so not sure if different but ours are 4 day tickets, and when you add water parks, you get 4 park days AND 4 water park days for very minimal cost to add water parks option).
I don't like driving in foreign countries, even if driving conventions are similar, so off site would not work for me, if I were in your shoes. It typically costs a lot more to rent a car in a country where you are not licensed to drive, so I don't think you'll get amazingly cheap car rentals like we can get from the US, here is the US. Insurance is likely higher for you as well. So something to consider, and it sounds like you are.
You definitely get more perks in tickets and free dining than most of us in the US will get, for staying on site, so I agree with those advantages. And FP+ pre-booking for a group of 5 would be worth it to me too. We don't yet use EMH much, so that's a wash for me. DME from airport is nice, but not a deal breaker for us either way, though if your kids still need car seats, that makes DME a good option (and makes off site, renting a car, renting car seats or worse, dragging car seats from Norway, abysmal in my mind).