While going home, I noticed that I had come without my umbrella.
Just clarifying: のに here is not meant as a conjuctive (meaning "although", "despite"), correct? Instead it's being used as 「(((傘を忘れてきた)の)に)」, correct? That is, first の nominalizes 傘を忘れてきた, and then に is tacked on the end to be used adverbially with 気づいた.
Is 「傘を忘れてきた」considered a subordinate clause in this sentence? If so: since it's in the past tense, does that mean that it is happening in the relative past of when the main verb (気づいた) is happening (so that the 忘れてきた happened even earlier than the 気づいた)? Or are they both uttered with the reference point being the present moment (as in English)?