Clueless? Maybe.
Spoiled? She didn't choose her upbringing.
Brat? No.
She may not know to the full extinct, but she does have some clue. After all, she did try to warn Min Gyeom not to go home because she knew that her father going to meet him was bad. If she was clueless than she wouldn't have thought anything about her father going to meet her brother. Honestly I was surprised that she at least knew enough to warn him. Besides, I'm pretty sure her father went to great lengths to make sure his second wife and daughter knew nothing of the abuse Min Gyeom faced. Who wouldn't be extra careful in his case?
I think Minji didn't knew a thing about her brother situation, but i guess that his step-mother might know.
Is it just me or is Minji a clueless spoiled brat? Not that her brother's situation is entirely her fault but at least she should get a better clue of what her dad does to him.