What's with all the people arguing about incest? Indou looks nothing like Kagami's mom and if they were related wouldn't Kagami have known that they are related?
In some asian countries it's normal to call a woman thats NOT RELATED to you 'Aunt/Auntie' and that's like a typical sign of respect to a woman older than you
Your main point is correct, but the appearance thing is irrelevant—one side of a family can look very different than another. Indou resembles her mother; who knows what her father looked like?
The real questions for me are: Who raised Shinobu?
She knows almost nothing about her parents (Chapter 1, p. 27), she has been living in the countryside with very little to eat, and she was not living with “another relative” (besides the aunt she mentions) (Chapter 4, p. 114).
I had been assuming that the “aunt” she continually mentions and to whom she is writing the letters was the same person who raised her. She wishes for her presence several times, mentions that she smells good when you hug her, and says that she taught her “with great zeal.” But the evidence now suggests that the “aunt” (who may not be a blood relation) is in fact Kagami’s mother, which seems completely incompatible with the way Shinobu was living.
Listen, I'll be frank with you: I've read up to chapter 15, and I know the answers to most of your questions -- but I can't recall anymore how much of my knowledge comes from the chapters we all have read already and how much comes from chapters that have not been translated to English yet. Just in case, I'll use the spoiler-hiding format.
Shinobu doesn't know much of her real parents. She lost them in the war, or something. She was raised by a family who were neighbors or relatives. They lived in abject poverty, and in fact that family planned to sell Shinobu to a brothel in a few more years. Kagami's mother made a deal with that family (gave them money, I guess) so that they would allow Shinobu to attend the academy. She also settled in that town for a while and taught Shinobu all she needed to know for the entrance exams. Shinobu took a liking to her and started calling her auntie, and has been writing letters to her ever since she arrived in Tokyo (it's implied she doesn't know her real name, only her address). Of course, Kagami had no clue about any of these things: she hasn't returned home or talked to her mom for years.
Why the Kagamis are so interested in helping the Indous, that's still a mystery, though the most likely answer is that the two families became close during the war (many people in both families were officers). The circumstances of the disappearance of Shinobu's mom are a mystery as well (Kagami and her mom talk about the subject in vague and evasive ways, very suspicious).