Although born and raised Canadian, Mum was actually using the American conventional system of naming family relationships as illustrated by this table of consanguinity:
This system for naming family relationships does contain a significant logical flaw. Consider yourself as attending a family reunion at which a centenarian reminisces to a mother holding a newborn baby. Very possibly, by this table, that centenarian and that newborn babe-in-arms could both be your first cousin thrice removed, an obvious absurdity. Similarly, if a distant relative previously not known to you comes up to you and announces, "I am your second cousin twice removed," you have no way of knowing which one of you is the junior relative and which the senior relative without the two of you actually tracing your family tree. This results from giving some relatives who are generationally senior to oneself and relatives who are generationally junior to oneself the same relationship name (red) while other junior and senior relatives are distinguished by differing relationship names (green), as pointed out in this highlighted table of consanguinity:
Dad's contention as to how extended family relationships should be named derived from his experience growing up in Wales before migrating to Canada. In fact, he argued that the naming of relationships beyond those of close family members had been invented in Wales. Whether that last is actually true, I do not know. When I attempt to reconstruct what I think Dad intended to describe in a table of consanguinity, I find a far more logical system for naming family relationships:
To Dad, when you attend that family reunion and witness the centenarian reminiscing to the mother of the newborn, that centenarian would be your second great grand-aunt while the newborn babe-in-arms would be your second great grand-nephew, absurdity removed. Similarly, if a distant relative previously not known to you comes up to you and announces, "I am your third grand-niece," you immediately know that you are the senior relative. In addition, the "... removed" modifier ceases to have any function and disappears.
Thus, I tend to side with Dad in this family pet disagreement and wish that the Welsh table of consanguinity could be conventional.