I'm pretty sure concubine are legal and even socially acceptable to men of his status. I think the only reason they are going through this charade is the mistress wants the power of a legal wife. And if a man shows such obvious disrespect to the order of things as favoring a concubines child and concubine over the legal wife and child, it's seen as a moral failing. The classism and hierarchy of a Confucianism relies on everyone knowing their place and acting accordingly. Students obeys masters, sons obeys father, wife obeys husband, concubine obeys wife etc. etc.