how did niang foil the children's attempt to write an anonymous letter of complaint about her to their father in chinese cinderella

I believe she spied on the children, and they never got the chance.

Niang asks Big Sister if she wants to move downstairs on the second floor. This causes separation between Big Sister and the others. This also gives the opportunity for Big Sister to be able to be loved by Niang instead of being yelled at by her.