I'm new to apex and am having difficulty with a test class for a working trigger and class in my sandbox.
The trigger and class I have work after insert and after update on a field value ('Stage') on a parent object. 
If the parent is new, then a new child object is created with a Stage__c field that mirrors the parent object 'Stage' field

I started writing a bulk test class, but as I couldn't get it to properly create new records, I started again from scratch with a single test record.
I insert the test record and a child record is created exactly as it should be. (System.debug, assert etc. confirm).

Then I take that same test parent record and update the 'Stage' field to a new value. The after update trigger should create another new child record with the new 'Stage__c' value and also find the old child record and update a field there. 

Even though System.debug says I've successfully updated the field 'Stage' on the parent object, the trigger is clearly not being called as it doesn't created a second child object.

I'm using oldStage.Stage = 'new value';  update oldStage;  

Guessing the Test environment never really 'saved' my initial record so it doesn't recognize this is a legit update. 

Can you help me understand best practice and solution(s)?

Thanks