multihosting 101 ... with apologies

I *swear I tried to find out how to do this very basic thing by looking
online, but apparently i don't know what it's called.

I have 43.XX.XX.XX hosting MyWebsite.org
There's a subdir called MyOtherWebsite, and I want requests for
www.MyOtherWebsite.com to use that subdir as the root.

Both domains point to the right nameserver. This is hosted on a VPS
machine, so I can do whatever I want to reconfig.

I thought this was to do with mod_rewrite, but that looked way more
complicated than I need; I installed a virtual-servers module for
webmin, but it's not functioning right. In webmin's normal Apache
module, I can't figure out how to make virtual servers behave this way.

All help is appreciated. Likely there's a very simple tutorial someone's
done that I just can't find. Thanks