In "coaxed a safe distance away", the phrase "a safe distance away" refers to where Rose went as a result of being coaxed.
English verbs of motion
The pattern that you see in the phrase "coax away" is very common in English verbs that describe motion, especially of Germanic origin. Many languages, like the Romance languages, don't have this pattern (and it doesn't work with many English verbs that come from Latin).
The pattern is: a verb of motion typically indicates the manner of motion but not the path or direction. The path or direction is indicated by a special word following the verb. Many words that work as direction words, though not all, can serve as prepositions in other contexts. Here are some more examples:
Rose ran away. (Rose ran to some place away from where she started.)
Rose walked inside. (Rose walked from outside some enclosure to a point inside the enclosure.)
Rose fled upstairs. (Rose fled from the ground floor and went up the stairs.)
Rose flew north.
Rose turned around.
Rose came home.
Rose wandered back.
Rose jumped ahead.
This works passively, too:
Rose was led away. (Someone led Rose to a place away from where she started.)
Rose was coaxed inside. (Someone gently persuaded Rose to enter some enclosure.)
Rose was driven upstairs. (Someone or something forced Rose to go up the stairs against her will.)
These direction words can form the nucleus of more-complicated phrases. For example:
Rose was coaxed ten feet outside the front door of the bank. (Rose was inside the bank, and then someone coaxed her to come outside the front door of the bank, and continue moving until she was ten feet away from the door.)
And of course, the same constructions work metaphorically:
Rose was coaxed out of her lunch money. (Rose was coaxed to give her lunch money to someone else.)
It usually doesn’t work with verbs from Latin
This pattern of "coaxed away" often doesn't work with verbs of motion that come from Latin:*
Rose entered inside. (This means that Rose entered (something) while she was already inside (some enclosure), not that the act of entering put Rose inside.)
Rose exited downstairs. (This means that Rose exited the building when she was downstairs, not that the act of exiting moved her downstairs. But "moved downstairs" does follow the Germanic pattern.)
ascend inside! Ascend up the ladder!" yelled Johnny from the treehouse. (That doesn't sound like English. The native English verb is climb: "climb inside" or "climb up". With ascend, you use a direct object: "ascend the ladder".)
Notice that these last three verbs denote the path or direction of motion, not its manner.
If you're curious to learn more about this, look up "satellite-framing".
* It's not a rule, of course. "Turn" is from Latin (actually Greek via Latin), and partly follows this pattern. "Turn" sort of denotes a path, and sort of denotes a manner of motion.