You seem to be almost there. Just a few things to point out.
In order to be able to tell you exactly what the に at the end of your phrase is doing, we'd need the rest of the sentence.
とれる can be translated into many words, but the closest meaning to the sentence (in my interpretation) would be: 1. to be interpreted as, and 2. collected.
Depending on context, とれる can translate as "be collected" in the sense of gathering something. (この川でとれた鮎 - the 鮎 collected/caught in this river; 裏の畑でとれたばかりのトマトを使用しております - We use tomatoes collected (picked) fresh from the field out back)
However, here, とれる is the 可能形 of とる and here simply means "can take (as)", or "can interpret (as)"
And I paid attention to the particle と and も that can be translated as (and also).
Be careful here. と is used in the same sense as "and" is in English ONLY when connecting nouns. Here it acts as the "(as)" in "can take (as)" and "can interpret (as)"; it's esentially defining the contents of the interpretation. By adding "も" after "と" we indicate that this is not the only thing it can be taken "as" (it can/could be taken as something else also). So 謙遜ともとれる on its own translates roughly to:
"(I/we) could also interpret as humility"
You seem to have correctly interpreted that "謙遜ともとれる" is directly modifying "妹の態度". Putting these together, we get, in slightly strange English:
"My younger sister's attitude that I/we could also take as humility".
rephrasing this into more natural English, I might say:
"The seemingly-humble attitutude of my younger sister"
So my translation is:
...from such a humble and also calm attitude of his younger sister.
While そんな does translate as "such", this is more in the sense of "that kind of". (In impolite speech, we do sometimes use そんな in the same sense as そんなに (i.e. "to that extent"), but that's not how it's being used here, it is being used to modify 妹の態度)
So if I were to translate your full sentence I might say:
"That seemingly-humble attitutude of my younger sister"