The EU didn't unify Germany.
Inclusion of Spain - politically OK. Economically not so great
Inclusion of the Balkans - as always a trip into the mire.
Eastern Expansion - Made the EU massively unweildly politically

I do not see how, barring Spain, any of the others how the EU has prevented wars / caused peace. The USSR and the USA brandishing nukes did most of this - but perhaps not such a nice fairy story.