Is your website mobile ready? If not it will not appear in Google search ranking. Google is stating that all websites must automatically adapt to a mobile friendly format, rather than be designed specifically for mobile devices. Mobile specific sites have the format m.website.com. Although normally a sub domain of the master site, in this example website.com, Google creates two indexes and often do not know which version to show the user. More details may be found at:-
Google provides a tool at the above link to test if your website meets their needs.
Obvious question is how do my two sites, this one on Squarespace and the other on GoDaddy using Wordpress and a Photocrati purchased theme do on the test?
So there you have it. The quick solution for me is to stick with Squarespace and abandon the "other site".