Well, that's not true, is it?
I say this as somebody who is paternally British and maternally Irish. My great-grandfather was in the Royal Irish constabulary, but his eldest daughter (my great Aunt), married a leader of the IRA. Most of my Irish great uncles came to England from Ireland and enlisted in the British Army and the RAF in WW2 while Ireland remained neutral. After the War, some of them returned to Ireland, some of them stayed in England.
The real picture of life on the ground is complicated, and I'm going to assume you are not living amongst it, by your use of "their" when talking about Ireland.
At the point of Irish independence it was decided that those parts of Ireland who majority wanted to be part of the Irish republic should form a republic, and those that didn't (the six counties of Northern Ireland), would remain part of the United Kingdom. And so it is today.
The 100+ years since have held multiple chapters in the story, including murders on both sides, terrorism in the UK (including an attempt on a sitting Prime Minister's life), oppression of republicans in Northern Ireland, and a hard-fought and wrung out peace agreement.
The current First Minister of Northern Ireland is the leader of Sinn Fein, a formerly proscribed (read: banned), party that was considered the "political arm of the Provisional IRA" (they are the terrorists who bombed PM Margaret Thatcher).
The way we got to that state was the Good Friday agreement in 1998. That allows people in Northern Ireland to express both their Britishness and their Irishness (yes, they can have both! In the same person!), without fear of reprisal or judgement, either culturally or officially. People explore their cultures as they see fit. They vote for people as they see fit, even if London doesn't particularly like the leaders they vote for. They live. And they have a say in how things should be.
There is no oppression of the language. Gaelic is slowly flourishing again in the Republic, and those who wish to use it in Northern Ireland can do so. There's no mandate for dual language road signage in Northern Ireland as there is in Wales, but there's no real ask for it either: at some point it might happen, in the same way the Welsh Language Act came about in 1993 (another sign of UK government encouraging self-determination - the Welsh Assembly).
Successive recent governments of the Republic of Ireland for their part are happy with this situation: the price of keeping the peace if the six counties were handed over to the Republic today would likely bankrupt the Irish treasury (and it would have been worse during The Troubles): it would break the Good Friday agreement, there would be a rise of terrorism and so on. They know they'd have to ask for external assistance, and then we're just back to the worst of The Troubles.
The vast majority accept the right to self determination is the way, now, and for the future. Over time, it's expected the appetite within Northern Ireland to become part of the Republic will grow within the population itself. This is because of demographic change: the unionist population is slowly becoming a minority (funny how when a Catholic demographic of Republicans are told not to use birth control their birthrate is higher than the Protestant population who do use birth control - I am here today thanks to this marvellous papal determination :) ).
One day, there will be a vote. One day, change will happen.
But it won't be because of something being imposed. Or an imposition being removed.
I suggest you do a little more research, and look into what's actually going on with the UK here. The history of it - as with the history of most things - is rich, complex, sad, hopeful, and lived. It's not a slogan. It's not a talk given by a politician at a fund raising event. It's not the quip given by a guy you hear talking about it in a bar or at a dinner table who never set foot in any of the countries he's talking about. Just be a bit more curious.