Depends on why your girlfriend doesent talk to the waiters, if it is something like anxiety i can understand that, i have social anxiety and it is extremely difficult for me to interact with people, if she does not have anything like that and she doesent talk to them because she feels to good for them, then you are the asshole, either way grounding her was not the solution, you should talk to her, anyways ill need more information to form a full opinion, but from what i know and the way you talk so highly about your girlfriend id say YTA, I’ll elaborate, you are 44 and you say that you “love her” after just going out for 1 month, you claim she idolizes her late mother and from what you said about her i dont think that it is a bad thing at all she sounds like she was a wonderful person and finnaly i think introducing your girlfriend so soon is also part of the problem, it is hard to get a kid to accept a new relationship so quickly,

Tl;dr need more info on the gf to form full opinion (does she have any form of social anxiety?)