Thanks for your comments on this thread.
The Premium Family plan is indeed for up to 6 people who live together, each person with their own personal account. Since every member has their own account, they can listen to their music whenever they want on their own devices, no matter if another member of the plan is listening, as they would be using their own account.
As @Alex mentioned above, what is not possible is to use one single account on more than one device at the same time.
Regarding the smart speakers, keep in mind that it's necessary to link a Spotify account to the speaker's manufacturer account, such as Google or Amazon, and this is required from both ends (Spotify and the manufacturer). Therefore, each Spotify account must be linked with an individual speaker manufacturer account and the speaker can only be used by the account that is linked.
In the case of Amazon speakers, for example, you can create an Amazon Household which allows you to have multiple profiles in the same account, and you can link your Spotify account to your own Household profile and use the smart speaker you want, even if someone else is using another one in the house.
In the case of Google speakers, you can set up multiple accounts in the same speaker via Voice Match.
If you have any questions on how those work, we recommend reaching out to the manufacturer's support.
You might also be interested in Spotify Kids. Right now, the Spotify Kids app is available in a few select markets, so no worries if you're having troubles seeing it. We hope to have it available in other markets soon!
There's an idea about adding Spotify Connect in the Spotify Kids app - we'd recommend adding your +VOTE and feedback in a comment there to show your support and contribute to the discussion.
We hope this sheds some light on this.