Northern Ireland is civil unrest, not a military conflict. The UK and Ireland were both members of the EU during the vast majority of the Troubles. The GFA, which created the peace in NI, was predicated on both being able to remain in the EU. This has obviously changed. The EU membership of the two countries had no impact for decades.

As for Europe at large, there is really no good evidence that dependencies on trade remove the incentives for war - as shown by WWI; see - The Great Illusion. The dependency on the US for defensive capabilities has meant that European states haven't had to heavily militarize to defend themselves, and any build-up by one country would create fear and uncertainty in neighbouring states that can't ascertain the true and future intentions of those states (i.e. Germany acquiring nuclear weapons and a large standing military, like most nations in its economic condition and precarious geographic position would do), and what their future capabilities might be. This normally would lead to a security conflict or an "arms race." As the US is now focusing more and more on East Asia, I expect this to slowly change.