I'd actually discourage using submodules, because it has its problems which you can read about in this article.
Instead, I recommend using npm packages. Since you're working with Node, you're probably already familiar with npm. You can either host your own npm registry for private packages in your organization, or you could make use of private 'git' npm packages. Since npm v1.0.26 you can specify (private) git URLs for packages. Read this article for more information.
TL;DR Don't use git submodules, using private npm packages.