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If you use more advanced bluetooth module like CSR8635 you can put AUX directly to it - so if you plug jack in, it would play from aux not from bluetooth. Also you have possibility to put there physical buttons like play, pause or even a microphone for calls.
Yes it would be a problem, it's simply connected bluetooth and aux to same channel without any weird circuit so it can only play one thing. Don't know why would you plug two sources into speaker, it's meant to be portable not connected to PC or something.