There was a nationalist movement back in the sixties claiming that all the Arab countries are brothers (I think it was sort of a movement against the colonialism which all these countries were suffering of). That period aslo witnessed the gradual independence of these countries and some essays of union (like between Egypt and Syria, for example). So there came the expression "brother country" or "sister country" دولة شقيقة .
I know it sounds weird in any foreign language, but at least you have now an idea about what it means. So maybe you can manage to express it in a better way. If I find any better suggestions i'll post them here.