Achilles found himself in a good place the last few months. He was trying not to let his anger dictate his actions. It took a lot of inner peace to come to terms with. His reaction to the editors the day before could have ended badly had this been him last year or any time before that. His temper had started to wane down in knowing he had a child coming into the world---to share that with someone else---he'd never been there before. He didn't want anyone to step in the way, not even his own mother, definitely not his father who he promptly ignored in order to keep himself in this zen-like state.
Achilles wasn't oblivious to Briseis' dislike of Polyxena, at least at first. He hoped that now she had mellowed out to the idea. Achilles needed something to take care of, someone to call home, Polyxena had become that light that Briseis had once been to him. It had to sting a little, but he wouldn't ever let her feel replaced.
As she came in the door he gave her a warm embrace as always, once the food was settled and out of her hands. He kissed her forehead in greeting and let her make herself at home. There was a time he pined for her and she refused to let herself get wrapped up with him again and it had stung. Achilles was just content with knowing that it was possible for him to love again.