Help with Parent Child records - In other apps

Conditional drop down to the rescue. So a great feature of Quickbase has what's called a conditional drop-down. (sometime we call it CDD) 

So, say your third table is called Work Orders and in creating a Work Order to be assigned out you need to choose the Department and then choose the Division. These are going to be look ups off those two respective tables so you build those relationships.  One department has many Work Orders.  One Division has many Work Orders.    

But the magic happens when you then edit the field properties for Related Department on hyour Work Orders Table.   Scroll about halfway down on the field properties and you will see a checkbox for conditional values. 

"The values in this field depend on a selection in another field"

Then in the first drop-down you select your data entry field for Division or Related Division and then on the second drop-down field you select to only show Departments matching that Division.  

You'll find this works beautifully and while it may not be so relevant in your use case it performs exceptionally well with very high record counts. So for example if you had 10.000 different choices for departments the drop-down list populates pretty much instantly based on the conditional filter.