Picard was still fooling himself that it was just a short favour to help an old friend.That was a breakup? I really didn't get that out of "I'll be back, in a few days. Maybe even less." (Even with her replying "Maybe even more.")
But the point was that she knew he wouldn't be joining her in a few days. She knew what Beverly really meant, and that was before she knew of the son.
Perhaps he still will join her. There was some ambiguity about his relationship with Beverly at the end of the episode. It didn't feel romantic too me, more like divorced parents who managed to make the transition to platonic friends.