Is this a reasonably proximate summary?
Wyrn considers what she did to be right as she and Arthryn disagree regarding how equality works on in practice. Wyrn believes that the People are best under a strong leader to guide them and a Divine Royal Family can give the People that strong leader consistently and while treating everyone equal is nice in theory, it doesn't work out so well in practice compared to the alternatives. Arthryn believes that everyone is born equal in spirit and therefore should be given fair treatment and opportunity to prove themselves. Some people may prove themselves to be better, but they are getting judged by their actions and not the circumstances of their birth. Those beliefs is what Born Equal is and Arthryn expects the People to carry out those beliefs.
Arthryn doesn't agree with the hereditary monarchy and considers it to be bad, but so long as the People are trying to do what is best for the People and it doesn't cross certain lines, she will tolerate it. To put simply, so long as the People are doing the monarchy for the good of the community (Communal Mandate) and they still treat others fairly and give them opportunity to prove themselves (Born Equal), Arthryn will let them be.
She has effectively told them that they can have their Divine Royal Family so long as it doesn't take priority over Communal Mandate and Born Equal. This is a problem for the People due to the conflicts between DRF and BE, but hey, that is their problem and not Arthryn's. Her problem is keeping BE around and if the People can find a way to keep both DRF and BE, then good on them.
Wyrn does acknowledge that she enabled Bronwyn's selfishness, but since the end result is a good outcome, that is an acceptable compromise and a lesser evil for the greater good. For that reason, she understands why she is being punished and considers a fair price for her actions.
Bronwyn accepts her punishment and that she did wrong by using her position to empower her family at the expense of the community. She got a good result, but she did it for the wrong reasons and she needs to be punished for that as an example for future generations. She isn't happy about the whole being a statue thing (who would be?), but she agrees that the precedent needs to be set.
With the People, Arthryn was unhappy about Bronwyn
using her position to empower her family at the expense of the community.
The end result was good, but the bad behaviour and motive needs to be punished because while it turned out okay this time, that may not be the case next time.
They also understand that they need to uphold Born Equal and not discard it lest they suffer the wrath of Arthryn. So the Royal Family is okay and for the best, but they still need to give people the chance to prove themselves and treat others fairly regardless of their birth.
@Oshha is becoming a goddess a possibility for her?
Normally, the answer would be no as while prominent, she isn't really done anything to get worshipped, but...
Though she does have the Godshaper at her side...
This. Bronwyn is prominent enough and memetic enough that if Wyrn decides that she wants her as a new sister, she could probably set things up to get Bronwyn as a new Arthrynite Goddess.
Bronwyn would certainly get Beauty as a domain if she became a goddess, but the others would depend on Wyrn.