I'm not really following the conflict. Mitsuki hasn't made it that obvious that she wants to move to the states or not. Joe wanted to, but didn't. The new lady wanted to, and left Joe to do so.
So is she just trying to get Mitsuki to go with her so that Joe follows suit? I can't remember any reason why they'd want to besides "that's where the music is."
From what I gather, Kanna saw that Mitsuki hadn't made a decision on her career yet and saw an opportunity to help her out while also getting petty revenge on her ex by snatching his niece away.
This has the bonus of creating a secondary conflict where Mitsuki will have to choose between a potential major career opportunity and Aya, which is a fairly classic dilemma.