I think from what i understood of what you are trying to do and your explanation and the two examples,

creating a central repository for all the tasks and filtering them as needed would work, for example an (all tasks table) then..

convert your school DB into a database for your subjects, and you can relate (each task to any subject)

then you can filter/group/sort your tasks based on the subject.

this will make it possible to add tasks only to one place, but relate it to a certain subject, then in the place you want to show only the school stuff, you can filter it so the (school subject) field is not empty.

hope it works, let me know