It remains logged in as long as Mopidy is running. As soon as you try to start playback on a second device it will stop playing on the first device. This is all built into Spotify, it’s completely fine.
Just don’t let your teenage daughter have the details - I spent ages trying to find why my connection kept dropping out when I got home for lunch, blamed Virgin, bought new wifi dongle, tried different router, then in school holidays no problem at all, realized she was entertaining the Sixth form on my Spotify account. Gone to uni now with her own student account.
It’s taken a while but I have successfully trained my other half to set the client on her ipad to offline mode when we find ourselves in back and forth fights over the play token. It’s almost a fun game.