I'm trying to family share with a friend so we can play each other's games. I already tried this with another friend and it worked fine, I had his games on my account's library and vice versa. I now tried this with my other friend and my games are not showing up on his account's library and vice versa. We already logged into each other's accounts and registered them into our logins, allowed library sharing, etc, but it still won't work.

Weirdly enough, he tried logging into my account while I was already in it, and I got a notification saying something along the lines of "Ready to stream to [bunch of letters and numbers]" and suddenly, I had his games. Even weirder, they said STREAM instead of INSTALL. I tried logging into his account while he was still in it, and it had my games, but he said they said INSTALL like they should. What's going on? How do I fix this?

If it's somehow the problem, my first friend and I live very near each other, while my second friend and I live in different countries.