"absolutt alene" is a term that means that she'd be far away from any other people, out in the woods, or in the mountains. I think english does it the same way, and you'd risk misunderstandings if you used it. "vil absolutt" are connected here, meaning roughly "is really determined"
Since absolutely is an adverb, it would not necessarily be wrong to be used to describe the word "alone", such as "She wants to live absolutely alone" Meaning she wants NO people around her, period. The sentence could also be written: "She absolutely wants to live alone" and it would mean the same thing (in American English, anyway). I would say that all three meanings should be accepted (the two I've mentioned, as well as the Translation.
"She absolutely wants to live alone" and "She wants to live absolutely alone" don't mean the same thing at all.
The former means she definitely wants to live alone. The latter means she wants to live completely alone.
As I understand it, this Norwegian sentence has the former meaning because 'absolutt' refers to the verb not the adjective.