We do not have any children of school age, youngest is 23yrs!!!
I would always send my children, especially of the ages your children are, to a local state school.
They will intergrate quickly and will have mostly Spanish speaking friends etc.
Children in Spain more often than not accompany each other all the way from kindergarten up to secondary and become firm friends. This is not always so with International schools as the name implies, come holiday times most pupils scatter to all corners of the world and language stability is not so. A lot of the International schools teach Spanish as a seperate language and if you intend living here do you really need that???