Is there any way to float one div over another? I mean actually make the second div hover over the first, I don't want it disturbing the first divs content at all.

You could use the z-index:

http://www.w3schools.com/css/pr_pos_z-index.asp

Yes, you'd have to use positioning and z-index to accomplish that.
The divs in the header of this site - www.mdnearyou.com are 'stacked' using this method.