Final Cut Pro Playback on audio and video choppy

As Tom says, I would delete the optimized media (probably taking huge amounts of storage space) and disable "Create optimized clips for multicam clips" in Playback preferences.

I typically make H.264 proxies at 12.5% for multicams. They still look decent and are much more responsive on a slower spinning drive. Select all your clips in the browser, right-click and choose Transcode Media... Set the Viewer View menu to Proxy Preferred and then when you're done, set back to Optimized/Original for export. Create optimized and proxy files in Final Cut Pro for Mac - Apple Support

What drive? A rotating HD? An SSD? How is it connected to your mac?

Three streams of ProRes from a rotating hard drive will stutter, of course...

Also: 100GB may seem a lot, but if you use optimized media it will fill very quickly.

How big is the drive?

Try deleting the optimized file, which should be switched off in FCP settings, and see if the video will play natively. If it still has trouble, try creating proxy files.

How much RAM do you have? What's the external drive? How is it connected and formatted? How big is the drive?

It's a spinning hard drive. Most of that model of LaCies seem to be 5400rpm. That's going to be hard pressed for multicam, especially in ProRes.

Did you optimize the footage? Have you tried using proxy versions? How fast is the external drive?

Will I get the same results if I move the media to a MacBook Air?

The default FCP settings is to optimized multicam media. This is an obsolete setting for most recent computers.