Ok, the reason he hates you is because Italians are by and large Catholics, and he is Protestant, Irish are also Catholics mostly.
Basically, I'll start at the beginning. About 800 years ago Britain invaded Ireland (it's actually a lot more complicated, but I'll simplify it)
Over time they assimilated Ireland into the Empire, but oddly enough, even though it was the closest colony to them, it gave them the most trouble. There were many failed rebellions. The British were very harsh rulers, they killed hundreds of thousands of people and during The Great Famine of the 1840's, they refused to stop exporting food from the country, and rather than hand out food for free, they made people work very hard for it. Over 1.5 million people died, and 1 million emigrated.
During that time, they began a series of 'plantations', which meant paying British people (usually Scottish) to come over to Ireland and take control of the land. Effectively making sure that the only people with any power were loyal to England. These plantations didn't really work except in the Province of Ulster, which is the North of Ireland.
In 1916, however, a small amount of Irish nationalists took control of the General post Office in Dublin , during what is called the Easter Rising. They held it for a week, and most of Dublin was destroyed in the fighting. The leaders were executed, and this created massive support for Irish freedom.
Finally in 1921, after a brutal Guerrilla war between the British Army and the Irish Republican Army (IRA), Ireland gained independence from Britain, but on Britain's terms. Ireland would be able to make it's own decisions and have it's own government, but it would still be part of the British Empire, and the North of Ireland would remain in the UK.
You see, Northern Ireland had a majority of Protestants, with Catholics in the minority, unlike the rest of Ireland, which is the reverse.
South Ireland than had a civil war between the pro-treaty and anti-treaty IRA. The anti-treaty wanted to keep fighting Britain and win better terms, but the Pro-treaty wanted to stick with what they had achieved. The Pro-treaty side won and the pro-treaty IRA became the Irish Army. The anti-treaty IRA stayed the IRA, but were made illegal in Ireland.
After the war, both Britain and Ireland stabilized. In Northern Ireland however, things were bad for the Catholics, they were abused by the mostly Protestant police force, the Royal Ulster Constabulary (RUC) and were denied voting, housing and employment rights by the Northern Irish government (Known as Stormont).
After years of sporadic fighting and rioting, huge riots engulfed the Province in 1969. The RUC were totally overwhelmed, and took the step of calling in the British army to deal with the riots.
The British Army however, had to face a new threat in the form of a new branch of the IRA, the Provisional IRA. They fought the British army for 29 years, from 1969 to 1998, leading to mass casualties on all sides, and bombs every day. The IRA conducted bombings in Britain and ambushed the Army on a regular basis. Massacres of civilians by all sides were common.
This period was known as The Troubles
Also part of the violence were Protestant groups, like the Ulster Defense Association (UDA, which your cousin in law supports) and UVF (Ulster Volunteer force). They typically shied away from all out combat, preferring to randomly target Catholic civilians. They were responsible for such things as the 1974 Dublin bombings, which killed 35 people, and the Shankhill Butchers, who killed up to 50 innocent Catholics by torturing them to death.
The conflict was finally brought to and end by the Good Friday agreement in 1998. While it didn't make Northern Ireland independent from Britain, it gave strong powers to Catholics as well as Protestants.
However, it's not over yet, groups like the Real IRA split from the Provisional IRA in protest at the supposed 'sell out'.
I myself had the misfortune of seeing one of their attacks, where they shot 2 British soldiers earlier this year.