If you are near a major town particularly in central or southern Spain, there are many 'international schools' that cater for a variety of ex-pat children, and there are also some British schools. You may have to pay fees to attend these. In areas where there has been significant immigration, primary schools are used to catering for non-Spanish children - I recall a teacher in malaga saying he had 7 european languages in his school.
I doubt that citizenship will be an issue preventing your children from attending state school, but residence might be - if you intend moving around, will you be in one spot for a school year at a time? And if so, how will you cope with two children living permanently in a camper van?