so I thought it would be convenient to be able to stream same music inside and outside at the same time.
If it were me, I'd go with that thought. You might want to think about how much quality, loudness and speakers you'd like the outdoor system to have. In outdoor home patio systems like this, stereo is many times no longer important, and actually doesn't make sense (due to no one sitting in a stereo sweet spot), so consider a mono system. You might also want to consider a (typical PA) 70 volt system. They're really easy to DIY. These 70-volt systems have all sorts of volume controls for outdoor applications. There's plenty of info on the internet to help you along with setting one up.