This is a discussion topic for the N4 Lesson 1 reading passages.
I really thought that “母は家にいなくてはならない人” meant the mom is a person who has to be in the house…
I’d like an explanation for why it isn’t read like that-- I had the same point of confusion!
Because there wasn’t an answer yet, I’d like to also say, that I don’t see why it couldn’t have this translation.
First, there might be confusion here between two verbs:
いる（居る） = to be (ichidan)
いる（要る） = to need (godan)
いない = isn’t there
いらない = doesn’t need
Second, the grammar てはならない can be translated “must be”, “has to be”, or “needs to be”.
So, for clarity, I’d say “mom is a person who has to be at home” is a more literal translation. But considering the given English translation, maybe it was a hiragana typo and they meant いらなくてはならない?
(In either case, note 1 needs to be cleaned up too.)
Thanks for the tag Fred. I am not sure what happened here. I believe the original hiragana was いらなくてはならない, but then we may have changed it to いなくてはならない to make it sound more natural (without remembering to also change the English).
Regardless, fixing it right now!