At what point did it become the norm for children to refer to their parents as "mother/mum" "father/dad" as opposed to their first names?

Yeah probably. It's something that gets addressed in a lot of intro-level linguistics courses, so I know it's discussed in a lot of the relevant textbooks. It's addressed in Historical Linguistics by Lisa Purse and Lyle Campbell which is one of the more commonly used texts. (Here's a link to the page on Google Books). They're also quoting from Jakobsen (citation at the bottom) who says the following:

Often the sucking activities of a child are accompanied by a slight nasal murmur, the only phonation which can be produced when the lips are pressed to mother’s breast or to feeding bottle and the mouth is full. Later, this phonatory reaction to nursing is reproduced as an anticipatory signal at the mere sight of food and finally as a manifestation of a desire to eat, or more generally, as an expression of discontent and impatient longing for missing food or absent nurser, and any ungranted wish . . . Since the mother is, in Grégoire’s parlance, la grande dis- pensatrice, most of the infant’s longings are addressed to her, and children . . . gradually turn the nasal interjection into a parental term, and adapt its expres- sive make-up to their regular phonemic pattern. (pp. 542–3)

That's from the following:

  • Jakobson, Roman. (1960). Why “mama” and “papa”? In Bernard Kaplan and Seymour Wapner (eds), Perspectives in Psychological Theory (pp. 21–9). New York: International Universities Press. [Repr. in Selected Writings, Volume 1 (pp. 538–45), The Hague: Mouton, 1962.]

The specific connection to the sound of suckling is just one view of a very specific part of the question, and many don't need to go that far but would simply point out ma and ba as being two of the earliest and articulatorily easiest sounds for babies to make, so parents jump at that as references to themselves. As quoted by Campbell in the linked work, it's addressing it from a strictly Historical Linguistics perspective.

So I'm not sure if that works for you as a source. You can likewise grab just about any Intro to Linguistics text and find it there. Unfortunately I don't really have any handy to be able to give specific page numbers or authors for. Hope the above works though.

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