It looks like the answer is to avoid Safari and use Atomic Browser which allows you to control how it identifies itself to web site.
I downloaded Atom and then didn't bother with it, sticking with Safari. Are there good reasons for me to try Atom again?
New iPad wifi + 3G 64GB
Paired with Macbook Pro
Backed up to iCloud
1. The option to identify itself as a desktop browser, so you don't get diverted to the mobile versions of some web sites.
2. The availability of tabs, which I like much better than Safari's Most Recent 9 feature.
3. I like the VGA output, although AirPlay (video) would be even better.
4. It is said to be faster, although I don't think dramatically so.
If none on the above interest you, stay with Safari. I changed mainly because of the first two.
Atomic browser is buggy on many forums. Using the Reply button to reply to posts fails to bring up the keyboard, you have to use the Quick Reply instead if those forums have it. On other forums, the Atomic back button often just keeps reloading the page you are on.
Jail broken devices can install "user agent faker" from cydia. Adjust in settings and make those mobile sites go away.
Another tip is to check the website to see if there is a desktop version. A lot of sites if you scroll to the bottom of the site will have a desktop link that will allow you to see the site non mobile.
Current Apple Devices:
iPod Touch 4th Gen-Black-8G-WiFi
Or you can try other apps like puffin, downloads hd or skyfire