I don't think the mom is really as dumb as she's portrayed in this chapter. It is quite likely that her mom just wants to preserve the harmony, or whatever she can get, of the family.
Accusing Emeralda and providing all those evidence at this point in time is a double edge sword. While it can drive Emeralda out, it will also isolate Paril and mark her as a scheming and dodgy character. This will put a strain on their family's relationship with their retainers and other nobility. This incident will certainly be heard in the noble circles.
In my opinion, Celest is just doing her best to diffuse the situation before it becomes irreparable. She's probably not doing the best job, but by stopping Paril from going further, this matter can be solved in private. Paril is too used to his life as a powerful CEO of a powerful company and forgot that her family neither has the influence nor the capital that she once had. She won't be able to go forward if she scares off people at this point when she and her family have neither the influence nor the money to back her actions.
In politics, before you want to do something grand, you must first have the clout to support your actions. Before that, you should bide your time and gather allies and capital to fulfill your objective. Paril is too hasty at this point due to not wanting to be married off.