@HarukaNazu I totally get you. It might just be easy character setting, to give contrast later on when the 2nd daughter truly gets herself in the deep end of sh!t creek and her always-doting, always on-her-side grandma finally turns on her completely or something to that effect? I mean you got an old woman who is stubborn and petty to the point of openly hating and neglecting (this might be a reach) her own flesh-and-blood grandchild because she didn't like said child's mother, even though that child is the higher in rank by birth right (!), then what do you expect, I think it's just cheap, easy character build.
If I'm not mistaken after years and years of reading historical Chinese romance novels, the second daughter, though she is grandma's fav, is social-wise still inferior by default to the main wife's child, she does good -> "oh, not bad for a concubine's child", she does bad -> "what do you expect from a concubine's child". In the period in time when marriages were largely arranged by parents and a woman's future solely depends on who their husband will be, if the father were to offer marriage proposal for second daughter to a highly respected man with good background, as his main wife (which I doubt second daughter would tolerate anything less), her and father dearest will be a laughing stock, not knowing their place. With her "performances", I doubt she would get anywhere near the emperor's harem. So..... *sip tea*
Alas, my knowledge of ancient Chinese culture stems from fictional works, so take my thought with a teaspoon of salt pls.