Use the group feature to create separate groups for each class. Then enroll the students from each class into the proper group either manually or by creating unique enrollment keys for each class and having students enroll in the correct class that way. By doing so you can filter assignments, gradebooks, etc etc etc by the class. I do this when I have multiple sections of the same class (I work in a high school setting) and it works great.
FYI, by doing this you only need one Moodle course that can serve both K2 classrooms. If necessary, you could add multiple teachers to the course if needed. The only concern is that both teachers would have the ability to alter course content so they'd have to collaborate well together to make sure they didn't write over each other's content.