AirPlay 2 is limited to 24 bit / 48 kHz, so not ideal if you want bit-perfect hi-res playback.
I don’t think any third-party software integrates Apple Music so you’ll have to control the Mac if you’re wed to that streaming service.
You can enable Screen Sharing on your Mac and use an app like RealVNC to control the Mac from an iPad. The thing to remember with VNC is that you’re using a mouse cursor to interact with the remote desktop. That means you’re dragging your fingertip to move the cursor to the right spot to click a button or select a row, etc.
I would use USB to connect the Mac to the ML 585.5.
I currently have a Mac mini pulling double duty as music storage and as a streamer for a living room system. I use an Android app called BubbleUPnP to send hi-res audio from my phone to the Mac.