This is not a problem, but a special use case in your development.
You need 2 different calls for the output of 2 different set of breadcrumbs. Either you can do it via creating 2 templates, 1 for homepage and other for the rest. Put the "without Home" call in the homepage template and put "with Home" call in the other template. Then assign appropriate template to the documents.
Other way is to use PHx plugin which provides a layer of conditionals in easy to understand manners and can be handy on things like this. Using PHx you wont have to use the 2 different templates. But relying too much on PHx could be a bad habbit.
3rd way is to do same thing, is to write simple snippet which determines the current page and outputs the appropriate breadcrumb call.
Choose 1 of them and you are good.
All the best.