I also feel that "with my own arms" is an odd-sounding phrase in English. First, "I held her IN my arms" is much more likely to be used. (Though one could argue that, if I were a policeman arresting her, I probably WOULD use "with" instead...) Second, since I wouldn't be holding her in anyone's arms but "my own," the use of "own" seems kind of redundant
EDIT 2 Aug 2019 -- A year on, I better appreciate the meaning of vlastní and why both "with"and "my own" appear in the English translation, although they seem a little strange in English in the absence of context.
I need some context here about where this kind of sentence would be used in real life. Like I could see something like I held her in my arms being something someone somewhere would say. But this specific one. . .is there some kind of grammatical context that I ought to know about or was there something lost in translation here
The idea of holding something with one's arms is really only used in extreme cases. For example, if someone had no hands, they might hold something with their arms. In 99.9% of cases though, it's in someone's arms. It really would be a very good teaching point to point out that the Cz instrumental can be used with the English "in" in this case.