It is something that shows its face occasionally, and after a while it disappears again.
So 私の中で is a set phrase, followed by 顔を出し, another set phrase. Could one replace the で with では instead, without changing the meaning, or are there any other connecting words/particles one could use?
If you changed で to では, the meaning would change in the same way it usually does when changing で to では: there would be an implied contrast with things that aren't 私の中. Fairly literal translation from a random contrast:
- ... ポテトチップスというものは当時の私の中では珍しくて、物凄く美味しいものだった。
... To me, at the time, potato chips were a rare and unbelievably delicious thing.
The writer is presumably using では because they are aware that potato chips are not exotic or even all that delicious. There is an implied contrast between their naive past self and more worldly people to whom potato chips aren't such a big deal.
In this case, では would be harder to make sense of, since the paragraph is about a 不満 that other people are not aware of and the self spoken of is the current self: what would the contrast be with?
I don't think there's anything else you could replace で with that wouldn't change the meaning here, either. Maybe に, but that feels off to me. (However, other people may have other intuitions.)
I am confused (unfamiliar) as to how the two set phrases back to back flow naturally, but I suppose this is a common usage?
I don't think that 私の中で顔を出し itself is such a hugely common phrase, but both 私の中 and 顔を出す in the metaphorical sense are. Maybe it would be easier to think of these not as "set phrases" but rather consider the whole thing as a regular old phrase, where most of the nouns are metaphorical? Consider:
- [カフェで] [コーヒーを飲む]
[Drink coffee] [in a cafe]
- [学校で] [試験を受ける]
[Take a test] [in school]
- [森で] [熊と踊る]
[Dance with a bear] [in the forest]
- [私の中で] [顔を出す]
[Show its face] [within me] (metaphorically)