If Ireland remained an integral part of the UK it would have a political impact on the rest of the UK.
in 1911 the population of Ireland was 4.4 million compared to 4.7 million in Scotland. Irish politics had already developed separately from the UK and John Redmond's Irish Parliamentary Party won 74 seats at the December 2010 election becoming the third largest bloc behind the Tories and Liberals.
Redmond's MPs supported the Liberals and enabled Asquith to remain Prime Minister despite the large loss of seats from the 1906 landslide.
However, the prospect of all-Ireland self-government was viewed with horror by Carson in Ulster and he rapidly mobilised support among Ulster protestants against Home Rule and managed to get an amendment introduced which effectively kept Ulster outside the Home Rule proposals. The Nationalists raised their own Irish Volunteers as the polarisation and radicalisation of Ireland had begun before the onset of WW1.
If you want to keep Ireland part of the UK there needs to be a way to bridge the positions of Redmond and Carson. William O'Brien, who formed the All-for-Ireland League in 1909, recognised the concerns of Ulster (unlike Redmond, who seemed to believe Ulster would just follow the rest of Ireland into self-government) and had warned Redmond as bfar back as 1893 that the concerns of Ulster needed to be addressed.
Let's imagine O'Brien is seen as a bridge between the two positions and he puts forward (as he did in OTL) an all-Irish settlement and after kuch negotiation and arm-twisting, Carson and Redmond agree in early 1914 to a version of Home Rule which has safeguards built in to protect the position of Ulster within both the United Kingdom and the new all-Ireland self-government whose remit would purely be domestic affairs and from which all religions would be excluded.
With the reluctant support of both sides, Home Rule comes into effect in late 1914 and in the aftermath of the rapid allied victory over the German Empire in the Franco-German War of 1914, there is some spirit of compromise and the new all-Ireland Assembly meets in June 1915 in Dublin.