Can I ask what you're viewing the resulting mobi to determine that it's not working?
I've just verified that my ePub with the dedication code:
<p class="dedication">to Jill</p>
and the following CSS
definitely works as expected when converted with calibre to mobi (and viewed with Kindle Previewer or an actual Kindle device).
Don't use calibre's viewer to test whether or not it's working.