Possibly important supporting cast. Whether or not the bully and moms will have a major role to play in the story remains to be seen, but the music teacher is certain to be a mainstay.
He's a former rising star professional with a deep dark past, now languishing away teaching as a music teacher in primary school out in the boonies. When the tiger mom learns of him, she goes out of her way to beg him to teach Shuuhei but he refuses. However, the episode ends with him taking note of Kai's particular talent.
I believe I can see where this development is heading, but (non-romance) shoujo is not a genre I'm particularly savvy about. Considering this one takes place across quite a stretch of time, it's bound to be pretty thrilling, with lots of twists, turns, melodrama, and hot piano action.