Exactly what you describe:
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A Love to Kill --- She dated first brother, then falls for second brother ... first brother is an obstacle for them.
Close:---
Scarlet Heart --- Several brothers fall for her ... She loved first brother, later left him and fell in love w/ other brother ... first brother is not an obstacle, but he is used as one later on ..... several other brothers also fall for her or befriend her .... Excellent writing!
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Scarlet Heart: Ryo --- Several brothers fall for her .... same plot as above, but concentrates more on the romance ... also, in this version, first brother tries to obstruct her love for second brother.
Not exactly what you ask.... but
still a
Female Lead Caught b/w two brothers :
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Lie to Me --- younger brother falls for her, she falls for the older one, it becomes a problem for the lovers getting together.
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I'm Sorry, I Love You ---- Older brother falls for her, But she loves younger brother at first.... later things change, younger bro still an issue.
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Into the Sunlight --- The two estranged brothers fall for each other's friend/girlfriend.
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King of Baking, Kim Tak Goo --- Both brothers like her, she caught in the middle.
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Moon that Embraces the Sun --- Both brothers like her, she's sees one as a friend and loves the other.
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Passionate Love --- Loads n loads of makjang, but good story still ... Two brothers fall for same girl, she caught in the middle.
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Happy Together --- I don't remember exactly, but I think two brothers fall for same girl and fight over her.... About the 5 siblings.
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East of Eden --- 3 main couples for the three brothers... one triangle dominates - but the two guys are the brothers of the male lead, not brothers of each other .... second triangle is b/w two of the brothers, but fizzles out .... Not exactly what you want, but lots of complicated relationships and triangle and brothers, etc... Excellent writing.
Movie: ---
Secret Love --- Twin brothers fall for same woman ... she marries one and has an affair w/ the other, or is it the other? It gets confusing, who's who.