"She is a woman who knows what she wants."
Translation:Sie ist eine Frau, die weiß, was sie will.
Yeah, "möchte" would be more accurately translated as "would like" but really, in this context, that's just a more polite way of saying "will", and the end result is basically the same meaning (I mean, if someone said "Ich will ein bisschen Ruhe" or "Ich möchte ein bisschen Ruhe", it's generally understood as both meaning that the person wants some rest and quiet, the connotation is just slightly different)
(The substitute for weiß if you can't type the ß letter is weiss, not weiS.)
The rule that "in a subordinate clause, the finite verb goes to the end" is a simplification.
In the field model of German sentence structure, a German sentence is composed of a Vorfeld, Satzklammer, Nachfeld with the Satzklammer consisting of linke Klammer, Mittelfeld, rechte Klammer.
(These terms are variably translated into English; "forefield, sentence bracket, endfield; left bracket, midfield, right bracket" is what I'll use here.)
Some of those fields can stay empty -- in particular, the endfield is often empty in simple sentences.
In declarative main clauses, the finite verb goes into the left bracket, putting it right after the forefield, in the second position in the sentence.
In subordinate clauses, the conjunction or relative pronoun goes into the left bracket and then the finite verb (almost always) goes into the right bracket, putting it after everything that's in the middle field (e.g. objects, adverbs, prepositional phrases).
If the endfield is empty, a verb in the right bracket will be at the end of the clause.
But if the endfield is not empty -- as here --, then the right bracket is not at the end.
Endfields are, generally speaking, for "longish" sentence components -- what counts as "longish" is often up to the speaker and may depend on whether one is writing or speaking and on how clear one feels the sentence will be if some part of the sentence is in the midfield rather than in the endfield. Thus, two sentence orders are often possible, e.g. both Ich habe das Buch, das du mir geschenkt hast, gelesen (relative clause das du mir geschenkt hast in the midfield, before the right bracket gelesen) or Ich habe das Buch gelesen, das du mir geschenkt hast (relative clause in the endfield, after the right bracket).
Sometimes, only one order is possible -- for example, a subordinate clause that serves as subject or object more or less has to come in the endfield (e.g. Er hat gesagt, dass er dich liebt rather than *Er hat, dass er dich liebt, gesagt for an object or Es steht außer Frage, dass er dich liebt rather than *Dass er dich liebt steht außer Frage for a subject -- here with dummy subject es to fill the forefield position).
In this sentence, I would judge eine Frau, die was sie will weiß as ungrammatical; it sounds wrong to me. Maybe it's theoretically possible, but the version eine Frau, die weiß, was sie will with the headless relative clause was sie will in the endfield rather than the midfield sounds immensely better to me. (For reasons that I can't explain, I'm afraid.)
That was pretty technical; still, I hope it went a small way to answering your question.
I know that’s true (“ich weiß, dass es wahr ist”?); the distinction mirrors the two verbs meaning “to know” that one encounters in a lot of European languages (e.g., “saber” and ”conocer” in Spanish; “savoir” and “connaître” in French). The trouble I have is with those instances where “kennen” is used for something other than just knowing a person, or even something inanimate (like knowing a word, for example, which I believe is also “kennen”). I suppose the lesson here is to err on the side of “wissen” in such cases, and become more familiar with the exceptions as they arise...
"Sie ist eine Dame, die weiss, was sie will" was marked wrong, with the correct solution stated as "Sie ist eine Frau, die weiss, was sie möchte". Is there such a big difference between "Dame" and "Frau" that it overrides the difference between "will" and "möchte"? (I was using the multiple choice answers).
In colloquial speech they can often be ignored, but in more correct spoken German, at least a hint of a pause will be made, to avoid ambiguity, and to make for a "smoother" sentence more than anything else. I think the computer voice dramatises the pauses here a bit much...in practice, the pauses wouldn't be nearly as pronounced.