Richard discussing Lorelai’s professional demeanor is uncalled for point blank, because it’s not his place to criticize her in that domain at all. His parental authority does not extend into her workplace, and he has no standing in the running of the Independence Inn. He was out of line.
It also makes it hard to sympathize with him when he bemoaned that he was a nuisance to his wife and a burden to his daughter. The fact of his presence was not the issue, the fact that he butted in to their established routines and undermined their expertise regarding how their days should be run was. If Emily or Lorelai charged into his office and rearranged his schedule, chastised him in front of his subordinates, and criticized his food and clothing choices, I doubt he would’ve been anywhere near so diplomatic as they were.