Getting cross-domain tracking right in Google Analytics is difficult. Even if you use Google Tag Manager. There are many known issues when cross-domain tracking iframes, for example.
Google Tag Manager implements the cross-domain tracking plugin quite handily via the Universal Analytics tag template, and often the easiest way to track links and form submits is to use the Auto-Link Domains option, as described in this great series of posts on cross-domain tracking by Bounteous.
