The map works fine on every other page except my homepage. Here I have a console message that says
Uncaught ReferenceError: wpgmaps_localize is not defined.
First, this is an error where the JavaScript file is being loaded from your cache (http://www.mywebsite.com/wp-content/cache/min/1/5d4c5d378c26776a2556b4ab4d19191a.js). Could you try clearing your cache and see if that helps at all.
Second, are you working on a local server? (mywebsite.com has no DNS entries).