[Lord Gothmog]

When Elrond left Middle-earth for the West, the time came for his childern to make their decisions as to which people they would have their fate joined to, Eldar or Men. The brothers Elladan and Elrohir seems to have been able to 'delay their decision' by staying for a time in Imladris with Celeborn. However, Arwen did not delay, she made her decision to join her fate with that of Men and marry Aragorn.

There are some choices that do not allow for one to recant or change. This was one of them, in making her choice to join with Man she closed the door to the West. The same decision (with the same result) was made by Elros and he was in a better position to recant his choise and travel to The Undying Lands He was almost in sight of them. This is why There is now no ship that would bear Arwen into the West. She was no longer allowed to go.

As for Gimli, we are not certain that he did go into the West as this is only what the Hobbits heard after Legolas left. However, even if he did do so, we do not know the reason why he would be allowed even as far as 'The Lonely Isle'. The only ones we know of for certain are Bilbo and Frodo, both of whom were allowed into the West to have a chance to heal in sprit before dying and leaving Arda.