Method to change browser User Agent based on site
Have you installed and used the Dolphin Desktop Toggle add-on? Is it not what you were looking for?

Although, not an automatic method, it does make switching user agents much less painful.

Else, you might also try accessing the mobile version of sites that render better by using their URL e.g. http://m.twitter.com or http://m.gmail.com or mobile.website.com etc.