[or ◎(normal)コーチだなんて、◎(written expression)コーチなどというのは、○(informal)コーチっていうのは]
ずっとお母さんがコーチだって嫌だ X (wrong)
These sentences is possible to be separated into the following sentences.
“ずっとお母さんがコーチ” entire of this sentence is doing a role of NP (noun phrase) in this sentence.
So these sentence are supposed to be translated into “I don’t want my mother to be coach for a long time.”
(In Japan,coach (コーチ) just means instructor of the club activity.)
This の grammar is called 「格助詞」(case-marking particle)
Strictly there are three usages of 格助詞 but in this case,this の is used express the relationships between nouns and nouns.
And furthermore,this grammar which is used to express the relationships between nouns and nouns is separated into 4 usages.
4,Superordinate and subordinate words.(上位語と下位語)
In this sentence,there is の between コーチ and club team. This usage is 4th one. Called 上位語と下位語(Superordinate and subordinate words.)
In this usage,this の is interchangeable with 〜である
So it means, “The club team which my father is coaching.”