The basis of O-lan's lifelong enmity for Cuckoo is that when they were both slaves in the House of Hwang, Cuckoo did not treat O-lan well (Chapters 20-22). Because of this, O-lan will not speak to Cuckoo, and Wang Lung must build separate kitchens for them when Cuckoo moves into his house.
It is interesting to note that while it is Cuckoo who facilitates the relationship between Wang Lung and his mistress Lotus, this is not the main reason that O-lan hates Cuckoo. In a clear illustration of the cultural mores governing the place of women in China at that time, O-lan, who has worked tirelessly by Wang Lung's side for so many years, can accept that he does not love her and treats her badly; she can even tolerate having his concubine under her roof. What she cannot let go of are her bitter feelings towards Cuckoo - the hatred and resentment against another woman who has dealt with her with cruelty and disrespect.