They wouldn't have issue with her singing the song, using the name. They may have an issue using the lyrics in your book.

You can write to them for permission when it comes to publication stage, and then talk money at that point. YouTube is not public domain, and often you can find links within that are not accessible because someone made the link shut down. But they pop up again overnight, and it would be a serious occupation to take all of them down.

Which might explain why publishers are wary of novels. If you start making a lot of money with that bit of lyric within your book, you'd be open to a bunch of lawsuits for not sharing that. If your book fails, likely no one would take notice.

In spots like YouTube, if someone starts making money from something that is copyrighted from someone else, then I'm sure it would come down much sooner and they would punish the infraction more heavily.

So let's compare it to pirating movies for a moment. You run a copy of something that is not your creation. You share it with a friend. They might not catch you today, but if you start showing bootlegged copies from your home and charging admission, that's going to come to light a lot sooner.

I'd use it now, make your novel the best it can be, and then talk to the publisher about it when that time comes.