usually てもらいたい means "I want someone else to do something for me"
not "someone else wants me to do something for them"
Your understanding is correct :)
So why can てもらいたい be used like that in the quotation?
You just have be a bit flexible and implement the above understanding to a "he said I said" situation.
Quoting your translation "I want someone else to do something for me", it goes like this:
From the parent's point of view, I (the parents) , wanted someone else (their kid) , to do something (stop doing creator stuff) , for me (the parent).
BLAH はね、 BLOOPたかったの
This pattern is not uncommon when a feminine person is trying to explain another entity's intention of the past. It's used in drama, anime, manga etc. due to the dramatic effect it carries.
Adding a question mark to the end would make it a direct question (and a totally different meaning). Without the question mark, the sentence sounds incomplete, which is intentional. So, we typically add a trailing ... to make up for the incompleteness, and then the female will follow up with another sentence to elaborate.
If I were to translate, it would be like:
BLAH you see, wanted to BLOOP
But this translation alone won't convey the dramatic effect of its Japanese counterpart. It's one of those patterns you'll get used to by watching girls confess/justify her friend's past actions. Or even her own, by using her own name.
Eg.
Smart person "Why is this answer so long? It deserves a down vote"
My mother "dungarian just wanted chino alpha to understand... (more to follow)"
dungarianはね、 chino alphaに理解してほしかった (more to follow)