How about a camping holiday abroad?
Eurocamp are one company (there are of course others)
http://www.eurocamp.co.uk/
These companies dont just do tents but caravans, chalets etc.
Most of the companies like Eurocamp provide EVERYTHING you need when you arrive (Tent already erected, kitchen facilities etc).
With all those kids a hotel is not really going to be suitable. But on a camp site they can run around, go to the play area, mix with loads of other kids, and wear themselves out.
You find on camp sites the kids make friends VERY easily around the play area so will often amuse themselves, giving you more free time..
Most European camp sites have swimming facilities, a kids play area, as well as shops, a bar etc etc.
If you get one near the beach/sea then you wont have far to walk to go for a swim.
This will probably be the best "strees free" holiday for a large family.
btw It has not been called EuroDisney for about 10 years, it is DisneyLand Paris.