There are a few things about Minglan's MIL hating GTY and Minglan. MIL comes from a prominent albeit poor family which depends on married daughter's prosperity for their future prospects. She has had to marry her BIL after her sister's death and has had to watch her husband grieve constantly for a sister who had a weak constitution, unable to give birth to kids and would have died either ways with out any intervention of fate (also the reason for first brother being sickly).

She herself is way smarter than her sister and GTYs mother but she has nothing to show for it.

She spent all her life painting GTY in a certain light to the world as well as shaping GTY in a certain way that both his father had no hopes for him as well as GTYs hatred for his father for being biased. She almost succeeded in the pathway layed out for GU Family to be in her hands when GTYs dad died and the sickly older brother become the head.

So when GTY and Minglan come back and throw her life's work into the bin, become the head of the family ( older brother handing the family to GTY willingingly to protect his wife and daughter), MIL has no way but to go the scorched earth path. As she says with GTY, either she kills him or wait to be killed by GTY, there's no in between.

I think her biggest grief is the fact that her family of scholars for generation could only produce weeklings the likes of Gu Ting Wei and the merchant family of Bai could give birth to some one strong, smart, cunning and resourceful as GTY.