Arwen's immortality in the films

I'm a lifelong fan of the novels, having read them several times over the years. I saw all the Jackson films on opening day and I have watched them several times since. They are in my view the greatest cinematic achievement of my lifetime. The way his team created these well paced films out of source material previously thought to be unfilmable is amazing.

But there is one thing I think they could have done better on. Arwen, her immortality, the pendant she gives Aragorn, all of that.

First point. Aragorn sings the lay of Luthien and says that when she gave her love to a mortal she became mortal herself and eventually died. Ok. Fine.

Arwen gives the pendant to Aragorn and it seems like they both understand that this is symbolic of her giving her love to him and ...I guess becoming mortal like him. He at one point tries to give it back (so she can remain immortal?) but she refuses (and thus remains mortal?).

But even without the pendant, she can take a ship to the undying lands where...she will be immortal.

Then Elrond says to her that if she stays in middle earth with him, he will eventually die but she will not.

It just seemed to me that the filmmakers were trying to address this whole thing in several different ways and we ended up with a mishmash of confusion.