The "one" could imply that of the alternates only ONE choice is possible, or permitted. "Which" alone could indicate several choices from the set of alterates could be selected in various combinations. Of course, speakers are often very imprecise about their meanings & intentions when saying "which" or "which one". Usually the context makes it clear if the choices are mutually exclusive or not. If it's obvious the choices exclude each other, than a speaker would say "Which" with the listener understanding there's a missing "Which (one)".
It's not normally a problem unless the speaker does say "Which one do you want", without emphasising "Which ONE do you want?", when the listener would like to make multiple choices. They'd have to recognize the mis-match & communicate more about what is possible and what is not.
This is an interesting syntax, though I've heard it's falling out of favor.
The purpose is to avoid ending a sentence with a preposition (from, to, on, etc). So rather than say
"...the car I am sitting in."
you would say
"...the car in which I am sitting.".
This can be confusing, even for native speakers, so it is becoming less common. I had a linguistics professor who used to say
"A preposition is a fine thing to end a sentence with."
The "preferred" syntax (according to an English professor) would be
"A preposition is a terrible thing with which to end a sentence"
which clearly sounds terrible.
Overall, you can impress people with your knowledge of this fancy syntax, but it often times will be more confusing than illuminating.
Best Answer
To imitate one of the best answers I've read here...
You have four possible ways to rephrase that sentence:
So, only your first alternative is correct. The second one will need from at the end of sentence. Please also note that the relative that may not pied-pipe.
You can find more details on 'pied-piping' in StoneyB's answer mentioned above.