I am not sure that it was clear that Gimli was going to the Undying Lands. Or if he was, then it may have been more like a Purgatory, as it was for Frodo. Even Frodo did not apparently stay there, since it is not in the power of the Valar to convey immortality on any mortal.
As for Arwen, I am not sure that she did want to remain, at least once Aragorn died. In Appendix A, as Aragorn prepares to die, it is clear that she now fully realizes the bittnerness of her mortality
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...and thus she tasted the bitterness of mortality that she had taken upon her.
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and she says
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...there is now no ship that would bear me hence, and I must indeed abide the Doom of Men, whether I will or I nill: the loss and the silence. But I say to you, King of the Numenoreans, not till now have I understood the tale of your people and their fall. As wicked fools I scorned them, but I pity them at at last. For if this is indeed, as the Eldar say, the gift of the One to Men, it is bitter to receive.
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And beyond this, she did not seem to cling willingly to her mortality, and in fact
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...Arwen went forth from the House, and the light of her eyes was quenched, and it seemed to her people that she had become cold and grey as nightfall in winter that comes without a star.
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I don't read this as a case of Arwen willing so much to remain behind (at least once Aragorn died) as now realizing the full bitterness of her situation...