Check a checkbox in table A if a condition in related table B is true

I've had to implement this type of thing several times.  

You will want an "Employee Days" table and a "Days" table.

Assuming you already have an "Employees" table, a "Shifts" table, and a "PTO/Vacation" table.

Then you can connect all the employee days records to the respective shifts and PTO records through a formula relationship.  Thus you can easily filter out the employees that are "out"