*reply to SPOILERS*
She has more than one interaction with her daughter. Ivanka is also (briefly) present in "If You Want Me" and "Sleeping," which was such a touching moment to me for them. I think the show is far more balanced than you give it credit for between telling Guy's story and Girl's story. Guy has far more songs, yes, but he also only has two characters from his background that he interacts with, while the Girl introduces pretty much everyone else in the ensemble into the story. One instance of this is, in the film the Guy takes her to a gathering of local musician friends of his, where they play "Gold," whereas in the show she takes him to an open mic with her flatmates, and signs him up for a spot. Yes, she still exists mostly to prod him along on his journey, but she also has a rich set of inner conflicts and mixed feelings within that purpose. To say they don't explore her character along the way is to miss a lot of the work Cristin has done, especially during "The Hill" (a song I rarely listened to on the soundtrack but was one of the most powerful performances, IMHO, in the show.)
My $.02 is all.
Words don't deserve that kind of malarkey. They're innocent, neutral, precise, standing for this, describing that, meaning the other, so if you look after them you can build bridges across incomprehension and chaos. But when they get their corners knocked off, they're no good anymore…I don't think writers are sacred, but words are. They deserve respect. If you get the right ones in the right order, you can nudge the world a little.