Late night, or usually written late-night is an adjective meaning happening or operating late at night. See for instance macmillan.
Late at night means during some time at night, quite far into it.
So you could describe yourself as a late-night worker (if you do it regularly) or you could simply say you worked late at night. This would mean you worked probably after midnight.
Another common expression is I was working late, one night, which means you were working later than usual (the same way as "he was late" meaning he arrived later than planned), at some point during the night (or evening).
Here night is used to mean evening, as in "the end of the working day", not night as in "when people usually sleep"!
The sentence in your first example gives me the feeling that the writer means indeed just that: she wasn't working late-night (which would indicate she was working after midnight or so), but one evening, she was working later than usual.
Your third version strikes me as Indian English - a turn of phrase like husbands checking their mobile phones in midnight may seem odd to speakers of AmE or BrE.
I don't know if the use of in instead of one or at is generally common or accepted in Indian English, but I dare say in AmE and BrE it is probably frowned upon.