explorador - 5:27 pm on Aug 24, 2013 (gmt 0)
There are diff ways depending on how you got your mobile and desktop version.
If you have the same content being served over the same URL detecting the device on the server then use a cookie, it should show and keep the right version for the user.
The feature you talk about "request desktop site" is mainly modding the user agent to tell the server "I'm a mobile device" or "I'm a desktop", this will work if you show your visitors the same url but you choose what to server on the server side based on the user agent.
The trick: it's not 100% guaranteed but mobile devices include the word "mobile" on their user agent string, desktop versions won't have that. I say it's not 100% safe because android is to fragmented you can find cellphone software modifications installed on tablets without that working as it should.