That Sun Family Madam Song mentioned earlier is probably indeed the Sun Family she knew about.
Yu State is not too small nor too big, especially with marriages between families not being uncommon. This intricate web of kinship relationships probably connects all the aristocratic families in Yu State if traced back three generations.
If that's the case, some things now make sense.
Madam Song hadn't mentioned anything about the Sun Family's birthday banquet when she arrived yesterday. She probably had no intention to go, as the birthday party is hosted by the Sun Family, the maternal home of the third Madam. How could Madam Song, as the second Madam, be in the mood to attend such an event?