G.A.
Oh they are smart little cookies, aren't they? Here's what we do: early bath, 15-30 minutes of a movie/show, then we go to his room, say prayers, and thats it.
Maybe you could get her bath done a little early and replace singing with something else, say tv or a few more minutes of play time. They understand more than we give them credit for, and I bet she will agree to give up the singing. Maybe stickers on a chart or something then a prize at the end of the week for going to bed easily each night.
I know my son will drag bedtime out as long as he possibly can, so we just have to be firm and not give in (which is so hard when they want one more hug...kiss...drink...)
Good luck to you.