A journey across Ireland
An escape from western counties would have taken place on foot. For a family carrying some possessions, and depending on the point of exit, it might have taken just over a week, perhaps ten days. A single healthy person might have shaven a day or two off the 180 mile or so journey from the Mayo coastline.
The book is a work of fiction but I do believe that the family originated in Mayo or Galway, most likely Mayo. Uggool was chosen as an origination point, essentially because it looks like an interesting place. Quite frankly, it does not really matter. The conditions faced by most Irish peasants of the time were universally difficult, so life experience would have been similar whichever part of Connacht they actually originated from.
You can see the fictional journey my family might have taken on the map below.
(The map is contemporary and please forgive the screen resolution.)
The Journey:
Uggool; Westport; Clogarnah; Castlebar Lough; Bacon; Ballyhaunis; Castlereagh; Plunkett; Strokestown area; Tarmonbarry; Longford; Royal Canal; Barry area; Mullingar; Enfield; Leixlip; Blanchardstown area; Dublin.
And thanks to Uggool for the inspiration: