One WordPress Install, Multiple Skins for Multiple Domains

I am currently working on a client’s wordpress install. We want to deploy a new site, utilizing some of the same content, and it would make most sense to manage this is one admin area, and link multiple themes and/or installs to the same database.

What is the best way to accomplish this?

a) is there a theme switching plugin, which could switch plugins depending on if I’m on https://www.mysite.com or subsite.mysite.com?

b) should I use two separate installs, and just point subsite.mysite.com at the same database, using a read-only user?