Wow - that's a long nap - that may be the problem - with a 3 hr nap, she's just not tired enough at bedtime. That may also be why some days she takes a nap and some days she doesn't - she needs less sleep than that nap, and so it's throwing everything off. It sounds like she's been a textbook baby in terms of A times, so I'm guessing she is in terms of sleep needs as well. At 2, the average nap is only 1.5 hrs, and then 11.5 hrs is the average night. I would definitely start shortening that nap - do it gradually - just 15 min every 3-5 days. She may initially be really unhappy that you woke her, but she will adjust and I suspect that will help your bedtime routine immensely.
also, still try to use either wi/wo or gradual withdrawal rather than beginning any kind of accidental parenting if she's having issues at bedtime. By continuing to go back for extra songs, you're just reinforcing to her that she should cry because then you'll sing another song.
hth
michelle