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The "EU" didn't exist 70 years ago, but it originated in the ECSC, a transnational trading bloc to prevent future trade-wars over access to commodities (in this case coal and steel, it still being the 1950s). The redrawing of Germany's borders after WW2 left a lot of potential for regional disputes to flare up, and it was the Treaty Of Rome in 1950 that defused most of them before they could start. That's where the "70 years of peace" claim comes from, and it has only ever referred to Western Europe - those national empire-states that spent most of the previous millenium killing each other.

"the EU did little good in Northern Ireland"

Hardly a surprise. Not just because the EEC had no such powers at the time, but even if it had, member countries of the EU are sovereign, and thus "Europe" cannot intervene in their internal affairs. Mostly, though this is because the Northern Ireland crisis predates the UK's relationship with the EEC.

The whole Northern Ireland thing kicked off in 1968 (the only surprise was that it had taken so long). The situation peaked in late 1969, and it was only the deployment of British Army troops in the province to protect the Catholic population that stopped the province descending into civil war (I say this even with the memory of Bloody Sunday; without the troops, things would have been far, far worse). Before this, things were so bad in early 1969 that the Irish government actually considered the possibility of having to stage a military intervention in Northern Ireland to create a protected enclave for Nationalist refugees within the province. (The Irish government papers are brutally honest about the slim chances of such an operation succeeding, but it had been planned for)

By 1973 when the UK (and also the Republic of Ireland and Denmark) joined the then EEC, the crisis had been largely averted. What remained was a domestic UK law-and-order issue, and as a domestic issue, the EU could do nothing about it. However, common membership of the EEC did give the Irish and British more opportunities to cooperate on resolving the problems - the fringes of EEC meetings allowed the governments to meet and talk about this without it carrying the weight of a "summit".

What the EU did do later was fund infrastructural links between Northern Ireland and the Republic - the opening up of access between Dublin and Belfast has done more for peace in Northern Ireland than most will give credit for.

I hope the UK votes Remain. We actually like our next-door neighbours more that we'll ever let on, and we really don't want to have to live with border checkpoints again on what would become the frontier of the EU in the event of an exit vote.