"I have always wanted to learn to play the violin."
Translation:Ik heb altijd viool willen leren spelen.
"Viool" is the direct object of the main verb "spelen". All the other verbs ("heb", "willen" and "leren") are auxiliary or modal verbs. The infinitives are all placed at the end of the sentence.
You could also write "Ik heb altijd willen leren viool spelen." In that case, you use "viool spelen" as if it were one verb (without a direct object). That is slightly less standard, I would say, but not wrong.
The way was thinking it is: "i want to learn X". X in this case is "playing the violin". So, ik heb altijd X willen leren, substituting X for 'viool spelen' I get "ik heb altijd viool spelen willen leren."
Yes, but you make this division at an arbitrary point. You might as wel say: "I want to learn how to play X", with X being the violin. Or "I want X", where X is learning how to play the violin.
I think it makes the most sense to view "spelen" as the main verb, not as part of an object.