I’m gonna reply to your post as I go along rather than do a mega reply.
I don’t think there’s a conflict between “social” and “interpersonal”. I read your use of “interpersonal” as indicating that you think morality is about other people and specifically about doing harm to other people. I read Rand’s use of “social” in context as describing the idea that morality is about other people, which she criticizes. So the connection between “interpersonal” and “social” is that they’re indicating the same basic idea about morality (which you advocate, and which Rand criticizes).
Your next clause, IMHO, clarifies your meaning: “and people are free to live their own lives (wrt themselves) how they wish.” So you’re basically emphasizing that if you’re not harming other people, you can do whatever and that’s compatible with morality. I disagree emphatically (as does Rand).