If I understood your question correctly you are looking for a way to hide left navigation (Quik launch) on most of site pages and show it just on pages of certain page layout. Important thing here is: What is commonly used scenario (or default scenario): navigation is visible or navigation is hidden? (I am assuming navigation is hidden)
The simplest approach I could think of is to override some styles in masterpage to hide left navigation, wrap those styles in some custom ContentPlaceHolder and then override it on targeted page layout. In my opinion by doing so you are making smallest possible change to achieve your goal.
In masterpage add new custom ContentPlaceHolder (I think that the best place is just before PlaceHolderAdditionalPageHead):
<asp:ContentPlaceHolder id="PlaceHolderHideLeft" runat="server">
Now you have navigation hidden on all pages that are inheriting masterpage.
Next step is to override ContentPlaceHolder in targeted page layout with .... nothing. So add following markup to your page layout:
<asp:Content ContentPlaceholderID="PlaceHolderHideLeft" runat="server" />
This page layout will no longer use custom style overrides and will display left navigation.