In light of the the mother’s own admission in the miss manners posting, she bears the lion’s share of the fault.
She by her own admission knew her D hated parties and yet, went ahead making plans for her graduating party while structuring the notification to her D on an opt-out basis when if she really took her D’s preferences into account…it should have been structured differently.
Would it have been too much for the mother/parents to allow the D the option to “opt-in” by asking if she wanted the party? And if she said no as is her usual preference…the issue could have ended then and there with no further complications. The opt-in versus opt-out is also IMO…actually respects the agency and places the decision making fully on the D rather than the opt-out when she could be effectively steamrollered by her overeager parents.
By making the notification to her D and the party opt-out as she did, the mother effectively created the conditions which nearly guaranteed this social fiasco was going to result.
While I also agree the D was rude for not coming or writing thank you notes, she wasn’t the main instigator of this mess…her mother/parents were.
For this reason, while her mother can use her parental cudgel to compel her to write apologies…using that cudgel does seem a bit hypocritical considering it was the mother/parents who engineered the very conditions which brought about the entire mess. And being the older parties…the onus/responsibility is overwhelmingly on them for this…not so much on the D.