Hey there #Steve: I have 3 DOT's in the house, lots and lots of Fires and 2 active accounts (no longer Family Library linked) - each and every device seems to perform individually i.e. asking for an audiobook to play on one DOT or Fire device does not impact or relate to any other device.
i would respectfully suggest that you contact Amazon Support Team again and find out what on earth is happening. :(
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I wonder why someone would follow their own alternative forum profile.