The McIlhagga clan in Ireland has been found almost exclusively in County Antrim, though there are rare references to Galway, Dublin, Down and Derry. One of the Irish Genealogical sites has just published the Index of Civil Births for the County of Derry where you can find just four McIlhaggas in the first decade of the 20th Century, namely:
Mary Ann 1906;
As you can guess these four were siblings. They were the first four children of James Spence McIlhagga and Elizabeth McGrillis. At the time James was a Railway Locomotive fireman. In fact the town of Coleraine, not far from Londonderry itself, was where Elizabeth was living when she and James married and presumably it was convenient for them to live there, probably in her home town and near her parents. Then after number four child, maybe it was his job - he eventually became a train driver - made it better for them to move to the central Antrim town of Ballymena, where their last three children were born.
Samuel (b.1910) and his wife Jessie went back to live in County Derry, in Portstewart, and his son Ronald James was married in Coleraine. A couple of years ago I wrote about a Jeannie McIlhagga living in Londonderry itself when she signed the Ulster Covenant in 1912.