HI SunHoney,
The period of time around the 1840s and 1850s were particularly hard times in Ireland. In particular there were food shortages, principally "the Potato Famine". During this period (and more), there was a lot of movement between Ireland and Scotland or England. From 1801 to 1922, the whole of Ireland was a part of the United Kingdom (of Great Britain and Ireland). Following the uprising in 1916 and a number of years of conflict, Northern Ireland was created from six counties of Ulster, and the rest of Ireland became the Irish Free State. Northern Ireland remained part if the UK (renamed as the United Kingdom of Great Britain and Northern Ireland, as it remains today). The Irish Free State became an independent country, later known as Eire or the Republic of Ireland. When (the whole of) Ireland was part of the UK, there were no immigration papers for those who moved from one part to another - it was merely moving around a country. The same applies for Northern Ireland after its setup. During the period when things were at there hardest in Ireland, industry was expanding in Scotland and England. Many Irish men became workers in the mining, shipbuilding, railway building and other heavy industries, which is where particular parts of Scotland and England became home to large numbers of families of Irish descent.
In Scottish census records, for someone born outside of Scotland, they were usually listed as English, Irish, Welsh or Foreign. Sometimes for England, Ireland or Wales, the census enumerator took more information than he was required to and you get a county or town name for Irish (or Welsh or English) folks. However, this was more the exception than the rule. As the census records are covered by a 100 year closure, and they are every 10 years, 1911 is the newest census that is available for us all to search. On that basis, Ireland was still whole at the time of these censuses, so Irish or Ireland on these records refers to the whole of Ireland, prior to partition.
Anyway, back to your folks. I did a search of the indexes on ScotlandsPeople (an index search is free nowadays). It doesn't look like any Southwell Fowler died, married or was born in Scotland; nor appeared in the censuses, so he probably stayed in Ireland rather than come to Scotland with his son. A search of these records for any surname appearing with a first name, gave Southwell as a middle name for some. One person appeared in the 1881 and 1891 censuses with Southwell as a first name (surname Lauther). Of all of these people with first name or middle name Southwell, none had surnames that you would consider as mis-spellings (or possible alternative spellings) of Fowler.
On looking at Francis (sr) and Elizabeth McKean's marriage certificate, the parents of the couple are as you have given. The other relevant fact to pick up on from that certificate is that they were married in the Roman Catholic faith. That makes a difference to the record sets you would be seeking in Ireland.
Between Francis (jr)'s birth certificate and his parents' subsequent marriage certificate, there are various spellings of surnames: FOULER or FOWLER, McKEAN or McCANE. In each case, the couple signed their names with an X-mark, so it is reasonable to assume that the spelling of the names were all from the registrar's interpretation of the couple's spoken words.
You have your work cut out for you tracing these folks in Irish records in an era where spelling was a varied thing.
All the best,
AndrewP