OK, It's time I deal with some major misconceptions here... firstly, it's a bad idea for you to use the XHTML Mobile Doctype full stop. As it currently stands, I don't know of a SINGLE mobile handset that actually either uses or acknowledges it, and as well intentioned as the W3C were, they built that Doctype back in the days where mobile devices were being weaned off of WML before the likes of the iPhone brought desktop browsing to the smartphone market and revolutionised the whole industry. Mobile XHTML is a dead horse and should be kept that way, it's just a restrictive incarnation of XHTML intended for a market that no longer exists.
Why you should use a separate design rather than having a stylesheet for mobile users is simple, like no mobile handset supports XHTML Mobile, very few devices support the "handheld" CSS at rule, and even worse, there's conflicting implementations as some use screen alone (like desktop browsers), some use handheld alone, some use screen AND handheld and some use CSS3 media types. All this along with the millions of different handsets with their own META headers make detection and redirection an impossible task, so just do your visitors a favour and offer the two different formats as their choice - it'll save you headaches trying to hack around it.