I have a django project managed with git. I am git pushing it to my host. Now, I want to be able to push just one of the directories (inc. all sub dirs) to another git repo.
Have you looked into git submodules? It allows git repositories to cleanly nest, but remain fully independent.
This means you can have a subdirectory with a different remote url for push/pull and different commit tree+log without cluttering up the main project.
https://git.wiki.kernel.org/index.php/GitSubmoduleTutorial