Japanese kindergarteners cannot enjoy haiku yet, but I think most of them can count "the number of sounds" in a word based on the mora system. See my answer in this question: Do native speakers think of prolonged vowels as one long vowel, or two vowel sounds following each other?
The mora system is important not only with classical poetry but also ...
Most probably your transcription is correct: もちあたぼうよ
It is divided as
もち - a contraction of もちろん
あたぼう - a slangy version of あたりまえ
よ - a particle.
Regarding よ, I'm not really sure which definition applies, but it may be 語調を整えたり、強めたりする意を表す. Essentially it does not affect the meaning.
On your question of how, colloquial expressions are often not covered in ...