Interrupted listening between devices

I am getting a popup while listening to iTunes music on my iMac, "You appear to be listening on another device" (something like that), I am requested to simply hit Play to continue listening. I also experience interruption of music on my car audio system which is fed by either an iPad or my iPhone.

Turnes out my grand-daughter will be listening to music at those times, if I hit the play button on my end, she will be interrupted. Obviously we share the same account, am I to believe that iTunes can only handle one device playback at a time?