There are some interesting thoughts on the issues raised above in these threads:
Why did Arwen do that?
and
Who buries Arwen?
That is not to say, of course, that the discussion should not continue here. I just thought that it might be helpful to link to some previous threads that have touched on these issue.
In the first thread linked to, there is a fascinating exploration of why Arwen would wish to leave her family to die alone in a fading forest. I, for one, found it quite difficult to understand why whatever it was that led her there should be stronger than her maternal bond with her children. On this issue, I would recommend
Mr Underhill's excellent analysis at post #35.
Edit:
Helen, you beat me to it while I was reviewing some of the wonderful posts on that thread!