gatsby11,
your eu spouse visa can only be issued in one passport. you can either have it in your nz passport or argentinian passport. if you decide to have it issued in your argentinian passport, then you enter spain as an argentinian, once you are issued your 5 year eu family member resident card, you can start applying for spanish citizenship after completing 2 years residency. process takes 2.5 years. you do not have to renounce your argentinian citizenship. regarding your nz citizen, how would they know you have it?