I'm playing Wind Waker on Dolphin too - and I haven't had a hint of this problem before. So have hope! You're not (completely) doomed!
A couple of things - first of all, the video you posted shows a ridiculously low framerate. If I'm not mistaken, that's evidence that you're using a built-in graphics card.
Surprisingly enough, a Gamecube can't really be emulated on a built-in graphics card - notwithstanding the fact that it's 12 years old - because like all gaming systems, the graphics card was the most powerful piece of hardware in there. I'd recommend getting a $50 graphics card from your local Best Buy - they're super-easy to install, and if it still doesn't work, you can return it within 14 days for a full refund.
Secondly, the way that your aim is sort of 'bouncing' in the video shows me that you're using a keyboard to play. Uh-uh. Ain't gonna cut it. That bounce is only exacerbating the glitch, and it's gonna kill you for the rest of the game. Luckily, this is solved even more easily - get a gamepad (you know, a controller) for 15$ from Target. Presto, your very own Gamecube/N64/PS/PS2/Whatever-system-you-ever-choose-to-emulate controller!
Thirdly, yeah, I realize that this question is two months old. You've probably already given up on your computer, bought that VGA adapter, beat Wind Waker, moved on to Twilight Princess, and started a fanfic novel about Link's unrequited love for Midna. But this is also for all those out there who download an emulator, boot up a game, and then go "Huh. This really isn't any fun." Because it should be fun.
Give me a few more paragraphs and I can tie this in with the American Dream, but let's just leave it at that for now. :D