Have you talked to Joe about this part?
She said, "We communicate differently, but there's nothing wrong with the way either of us do so." Um, in my book, if you're not trying to hurt somebody with your word and you do so, there actually IS a problem with the way you communicate.
If he is telling you she has poor social skills, is he also telling her this? Is he aware that she has no plans to try to change her behavior towards you, but instead thinks her communication skills are fine and tries to excuse it as "miscommunication"? (Taking, at best, half responsibility and trying to put the rest on you)
If he chooses to be in a relationship with someone who has poor social skills, that's his choice, but you do not have to be friends with her or even spend excessive time with her. Especially since you all live separately, it shouldn't be too difficult to exercise your option of, "I do not want to be around someone who repeatedly hurts me, regardless if that's their intent or not. Our scheduling will need to take that into account from now on." Being respectful and civil when necessary is enough.