Wordpress - How to set two different themes on one WordPress? (Desktop vs. Mobile)

To employ two entirely separate themes is a suboptimal architectural approach.
Themes are activated site-wide/globally and not on a per-user basis. You don't want to change the current theme constantly.

While I personally really dislike this option, WordPress ships with a function that sniffs the UA-String, wp_is_mobile.
This function can be employed to either output alternative markup and/or load an alternative stylesheet (from within the same theme).

Or - and this is my personal choice - familiarize yourself with CSS3 mediaqueries.