That's a clear path forward for Yuu & Haru--even better, it'd force her mother to acknowlege how far Yuu has come, and how worthy she is of notice from the parent who walked out on her.
Of course, the potential for Mom to simply bar Yuu from auditioning exists. That would depend on whether she's truly petty/vindictive/an otherwise actual antagonist in the story--but no use getting into that when it's just unnecessary to speculate on at this juncture.
Haru being a reliable means of calming Yuu's nerves like this is a great little visual signifier of their current relationship. Comfortable with close contact, it's only a matter of time before things escalate between them. Hopefully it happens when Yuu isn't stressed as well, at least sometimes.
The sister has been thinking of Yuu, then. And with Yuu joining in on the singing now, she's now aware of her progress--and more importantly, that negative reaction to Haru's existence at Yuu's side means future conflict. Not only is Yuu at odds with their mother, perhaps Sister remains attached to Yuu, even in absence?
I could see a plot line wherein Sister tries to break them up, offering to take Haru's place at Yuu's side--maybe declaring that the audition will go better, and Mother will accept Yuu more if the sisters do it together.
And that would compel Haru to step further out of her passive self and fight for what she wants, giving her a chance to show how much she's changed in her time with Yuu.
Will have to see, but interesting developments and options going forward.
Thanks for the TL as always.