Same problem...Invitation to family prompted me to sign up, downloaded to primary user under my sign in name (showing I'm in my individual acct.) and kicks the primary user off when I want to listen to my music. Very frustrating.
If all members use the same login information in their devices, your music will cutoff like it has been happening to you.
Each family member has to have a separate username and password, so the first step is to create new accounts for each new member (if they haven't already).
I suggest creating it with an email address (not the one used for Facebook, if possible), since they'll be able to pick a Spotify username / password. Using Facebook will not let you do that.
Each member will now have a Free account, so the next step is for them to join your Family plan through your account (You're the one who pays, so you'll be the Family Admin).
Send by yourself the link generated through INVITE WITH LINK, instead of letting the system send the mail.
Let them accept the invite logged in to the website and the app with their own username, and you'll be set. Each will be able to listen to music at the same time, and will have separate libraries, playlists and friends.
Hope it helps. 🙂
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