Can I run command from a program thats based on the root host from a containerized application?
This StackOverflow question has answers that could be useful for you, in particular, mounting parts of the hosts filesystem containing the host application.

But really, it doesn't seem to make much sense to run an application in a container and then try to directly access the host system. It seems to defeat many of the reasons to containerize an application in the first place.

It'd probably much better to put the required application in the container, along with Django. I see no reason why your container wouldn't be able to run docker itself (even though for some CI/CD use cases sibling containers are preferred over docker-in-docker approach).