What to do about whining?

Since Addi will be three in less than a month, I guess she has decided naps are overrated.  She refuses to sleep at nap time.  Her newest thing is to sit in her room during nap time and play quietly, "read" books and sing songs (which is fine, though I REALLY  wish she would nap because she gets so incredibly cranky later in the afternoon).  Funny sidenote: Somewhere during the course of this time, she also decides to undress herself...completely.  I don't know why she does this...her room is not hot, her clothes are clean and comfy...the girl just likes to be naked.  She would love it if we let her run around with no clothes on all the time.  

Anyway, back to the naps...so as I mentioned, she won't nap and then gets cranky.  The crankiness leads to whining.  MAJOR whining.  I guess if two is the year of tantrums, three must be the year of whining.  We have a 30+ minute drive to church.  Tonight, she literally whined herself to sleep on the way to church (constant, non-stop whining for at least 20 minutes).  I can handle tantrums, but I am clueless about what to do with a whiner.  If I try to ignore her, she just gets louder.  I know I shouldn't cave and give her what she wants while she whines because she will continue to do so.  I guess we could send her to time-out, but that doesn't seem to help with most other issues.  I AM CLUELESS and now that I look at this post, I guess I am doing what she does...I'm whining to you, my blog friends...oops. ;)  I said all of this to say, HELP!!! If anyone reading this knows what to do with a whiner, please email me (jennturner05 at gmail dot com) or comment on this post.  

Phew...parenting definitely keeps me on my knees...but I wouldn't have it any other way!!!