You can actually change a hidden setting so your galaxy tab2 will always choose either mobile or normal websites.
It was a pain in my b** too to get the browser to do this like i wanted and i spent a lot of time on trying and retrying, but this is how to do it :
This setting will sooner or later dissapear and you will have to redo this pain in the b**-selection. Also sometimes, your browser will reload your last choice automatically. That's why it's a good idea to clean history and
buffer in the settings of the standard browser first. (Go to SETTINGS in the browser, then select 'privacy and security'.
To change the type of browser choice :
1. Go to the standard browser window. Then enter 'about:debug' in the address bar in the browser. Press return. Nothing happens now, but you will have more possibilities in SETTINGS after doing this
2. Select options at the top-right corner of the screen
3. Select "Settings"
4. Choose the last option in the list on the left which is something like "Debug"
5. Select "UASTRING"
6. Then choose ANDROID for mobile websites, choose DESKTOP for normal websites.
Have fun ! :-)