All they needed to do was show her talking back to Gil-Galad telling him that she really didn't want to go and him insisting. Or she could have said, "I'm not sure I want to go. Though I yearn to see Aman again and the loved ones I left behind, there is still much I need to do here. Sauron is yet to be found." Or a number of other ways.
Indeed. If they wanted to show she's conflicted about leaving, there were several ways to do that that were more consistent with the show than have her jump from a ship mid-Atlantic and... swim back home, while all the other elves on the ship just ignore her instead of shouting "elf overboard" and tying to save her by stopping their ship, trying to throw her a rope and so on. I know the scene where she escalates a frozen cliff in the beginning establishes she's strong, but not "divine-like strong", just "heroically strong". Swimming across an ocean as a sensible mode of transportation is a step farther. If it's an act of desperation, it establishes her as clearly nuts. And I feel it may be the case, if we disregard every other source of information.
1. She's been seeing Sauron's influence for millenia without tangible proof
2. She's been so focused on that hatred that she forgot to inquire seriously about the fate of her husband (unless he's really dead in the show)
3. She was so angered that Adar rightly told her that if she wanted to see the heir of Morgoth, she only had to look in a mirror
4. Even without Adar pointing that out, the quote about the fate of Uruk is enough to put her in the villain side of the story
5. She proposes to travel thousands of miles on horseback with a fatally wounded person without putting him on a cart (thanks Eru it was Sauron and not a mere Southerner...)
6. She fumbles the opportunity to warn everyone about Sauron, sure "he left" but she should have asked for guards to scout the area and kill him on sight and sound the alarm immediately...
7. When she's put on a ship toward the ultimate mental healthcare institute (Valinor) she tries to commit suicide instead of accepting help.
This is a bleak depiction, but one that doesn't jive with her being the main protagonist of the show to be so emotionally and mentally broken.