You need to omit the Resigned by scripting a find; I suggest using Constrain Found Set because it then can be used easily even if you are working with an existing found set. Since you added 'unless specifically requested' you must include that option for your users. I would provide a button called 'Exclude Resigned' or ask in a Custom Dialog whether to exclude Resigned and branch accordingly. You would not need to worry about omitting the Parent's child records since, if their parents are omitted, those parents children won't be included either.
Create a script called 'Omit Resigned' and it will be:
Constrain found set [ ] then click button 'Specify Find Requests' , New, at the top change from 'Find Records' to 'Omit Records' and below left, find your Status field and select it. Then over in Criteria, type Resigned (don't put quotes around it).
You can now script to include this sub-script in other scripts or place a button with it on layouts. If you are on a child layout, this script will still work if the parent table occurrence is the same and, since it would be a primary relationship, it should be the same. Here is one sample on using it within a script to generate a report:
Go To Layout [ report layout ]
... here perform your regular find, such as finding records for a specific time period
... now with your found set, ask the question
Show Custom Dialog [ Yes ; No ; "Do you want to exclude Resigned?" ]
If [ Get ( LastMessage ) = 1 // user selected yes ]
Perform Script [ Omit Resigned ]
... do anything else such as sorting your report etc.