I sorted it out. Going to outline the steps I took so hopefully it helps someone else struggling with Dreamhost!!
Assuming http://www.mainsite.com is your main site, with the second site being at http://www.mainsite.com/parkedsite, with a domain of http://www.parkedsite.com; also assuming you've already got the MU Domain Mapping plugin installed and set up:
1. Point http://www.parkedsite.com's A name to the IP of http://www.mainsite.com
2. In Dreamhost, add http://www.parkedsite.com as a domain, mirror http://www.mainsite.com, AND park http://www.parkedsite.com (no one seems to have included this in ANY tutorials I've seen; I only found it after days of Googling, in ONE comment somewhere, so I tried it and it worked!)
3. In WP Admin panel, add http://www.parkeddomain.com to the site you want it to point to.