>>> I want to watch all 100 episodes of Stargate: Atlantis on Christmas day
100 x 44 min = 4400 mins = 73 hours 20 mins.
I think that you might need a bit longer than Christmas Day to watch all of it!
To return to your question though (hopefully with my brain in gear this time) . . .
The Chrome operating system doesn't have the codecs that are needed to read optical discs, so you can't use an external drive to play DVDs on it.
Therefore you're limited to using your laptop. I'm assuming that it's running Windows 10 which, unlike earlier versions of Windows, doesn't come with the software for playing DVDs built into it. If Microsoft had their way, you'd end up paying £12.49 to buy Windows DVD Player from the Microsoft store but, fortunately, that's entirely unnecessary as there are plenty of free programs that can do the job just as well, with VLC being the most popular.
So you need to download and install VLC (unless, of course, you've already got it on your laptop anyway):
https://www.videolan.org/
Once you've done that, plug your DVD player into a USB port on your laptop. (You might see a message saying that Windows is installing a driver for it. If so, simply wait until that task has been completed).
Insert a DVD into the drive. It might play automatically. If, though, you're presented with a dialogue box, asking you what you want to do with the DVD, select the option to play it with VLC. If you don't see that option, close the dialogue box (if it appeared at all) and open VLC. Click Media > Open Disk > DVD and click the play button.
Your DVD will initially play with control buttons at the foot of the screen but there's a 'Full Screen' button down there. (To exit Full Screen, press Esc).