I'm not sure whether you misunderstand the English expression or the book. I understand “*I don’t want the proposition that she goes” and “*I want she not goes” as expressing the same meaning, but I'm not sure about what you're trying to say with the first one because it has the same issue as the original regarding negating “I want”.
If I want her to go, I can say “I want her to go”.
If I want her to stay, I can say “I don't want her to go”. I could also say “I want her not to go”, but it's slightly awkward.
In the middle, there's the case where I'm indifferent as to whether she stays or go. In this case, I can't say “I don't want her to go”, because it's interpreted as meaning ”I want her not to go“.
To put it in a vaguely mathematical way, “I don't want her to go” is I-want(not(she-goes)). Grammatically speaking, this sentence is the negation of “I want her to go”, but semantically, it does not mean not(I-want(she-goes)). That's what the book is saying: the syntactic negation of the modality “I want” has a narrower (more specific) meaning than a literal reading would suggest.
Orally, if you emphasize the auxiliary, then the meaning shifts to not(I-want(she-goes)); this usually requires an additional confirmation or clarification. Depending on the context, this may or may not carry a slight preference for her not going.
I don't want her to go, but I'd prefer it if she did.
I don't want her to go. I thought it would help, but it's fine if she stays.
Some adverbs can convey the same impression: “I don't particularly want her to go”, “I don't particularly want her to go”. There are of course many other ways to convey indifference or a mild preference, such as “I don't mind if she goes”, “I don't care if she goes”, etc.