You can't (shouldn't) use underscores for css class names.
Also, first-child actually gets the element only if it is the first child of its parent, which it is not in this case.
One way to get the div you want is:
.mdf_widget_form > div:nth-of-type(2){}
also:
.mdf_filter_section.business{}
(but don't use underscores)
EDIT: Another solution (detailed explanation in the link in my comment)
.mdf_filter_section {background: red;}
.mdf_filter_section ~ .mdf_filter_section {background: transparent;}
This would make all classes selected have a red background, then overwrite all following siblings to transparent background, this works pretty well if you don't have too many css properties to add to the first class. (transparent could also be inherit or similar)