How to translate the Home link when using Path Breadcrumb?
Make sure you have the Variable module installed/enabled. If you also have the 
Path Breadcrumbs module enabled (as seems the case in this question), then there will be an extra tab within admin/config/regional/i18n/variable of your site (tab title = Path Breadcrumbs).

Within that tab, there are over a dozens of options available for marking them as milti lingual variables. The "Home link Title" is one of them, and probably the one you need to enable here.