mongoose,
Adding a sound absorbing panel will improve the acoustics of your practice room without blocking the sound from going through the sliding glass door, walls, etc.
To achieve any significant reduction in sound you need to block and absorb the sound in an air-tight, enclosed space. I take it you're not interested in building a room-within-a-room. So, that limits what you can do. Select a room with no windows, if you can, and furthest away from your closest neighbor.