As mentioned in the title i want to know if it is possible to switch from mobile version of a theme to desktop version but without having a separate theme for mobile devices. And to be more specific i mean like there is a button to change from mobile to desktop version.
Yes, what you looking for is a theme with "responsive design", which means the theme will change depending on the size of the screen.
If you google responsive design you will get some examples of it. There are alot of themes you get for magento that are responsive, but converting an existing custom theme to a responsive layout can be expensive
Updated due to original question being changed
If you do have a responsive design then you could use something like this:
Please check this Following URL
What are the differences between your "mobile" site and your "desktop" site? Is the content different? One solution could be to create a separate site to be your "mobile" site and name it m.yourwebsite.com or whatever. Then on your homepage your buttons to switch between the two would just be hyperlinks connecting yourwebsite.com to m.yourwebsite.com and vice versa. Is this what you're going for?