Rajiv,

Please see below for my updated code:
 

trigger CCList on Case (after insert, before update, before delete) {
    class CaseTriggerUtil {
        void handleCCFieldChangeEvent(Case [] argCases, Boolean argIsDelete) {
            Set<ID> lDeadParentIDSet = new Set<ID>();
            Set<String> lUniqueCCIDSet = new Set<String>();
            List<CC_List__c> lNewCCRecords = new List<CC_List__c>();

            for(Case lCase : argCases) {
                if(argIsDelete) {
                    lDeadParentIDSet.add(lCase.id);
                }
                else {
                    if(lCase.CC_List__c == null || lCase.CC_List__c.trim() == '') {
                        lDeadParentIDSet.add(lCase.id);
                        continue;
                    }

                    List<String> lCCValues = lCase.CC_List__c.trim().split(',');
                    
                    for(String lStrCC : lCCValues) {
                        String lStrChildRecUniqueID = lCase.id + '_' + lStrCC.trim();
                        lNewCCRecords.add(new CC_List__c(Related_Case__c=lCase.id, My_ID__c = lStrChildRecUniqueID, Email_Address__c = lStrCC.trim()));
                        lUniqueCCIDSet.add(lStrChildRecUniqueID);
                    }
                }
            }

            if(!argIsDelete) {
                Database.insert(lNewCCRecords, false);
            }

            delete [SELECT id FROM CC_List__c WHERE Related_Case__c IN:lDeadParentIDSet OR (Related_Case__c IN:argCases AND My_ID__C NOT IN:lUniqueCCIDSet)];
        }
    }

    List<Case> lCases = (Trigger.isDelete ? Trigger.old : Trigger.new);
    new CaseTriggerUtil().handleCCFieldChangeEvent(lCases, Trigger.isDelete);
}

I ended up doing the following:

Changed the object name "CC_List_Object__c" to "CC_List__c"
Created an autonumber for CC_List__c Name versus text
Changed the field name "Case__c" to "Related_Case__c"
Added a new Email_Address__c email address field to the CC_List__c object
Added in the following additional code to line 22:

Email_Address__c = lStrCC.trim()

The code is firing brilliantly, adding in each parsed CC record to the CC_List__c object upon save of the related case. With that said, each time I save the case, it resaves all values instead of just the new additions. Example:

If I enter in: 

CC_List__c (field) = abc@corp.com (text)

Then the object spits out:

CC_List__c (object) = abc@corp.com (record)

If I update the same case to:

CC_List__c (field) = abc@corp.com,xyz@corp.com (text)

Then the object spits out:

CC_List__c (object) = abc@corp.com,abc@corp.com,xyz@corp.com (records)

As shown above, the abc@corp.com is listed twice within the CC list, despite only be listed once in the CC_List__c field. Each time I save the record, the CC_List__c field inserts records into the CC_List__c objects as if they were new.

Any thoughts on how to handle? One thought I has was that each time the related case record is saved, it deletes all CC_List__c object records that have it's Case listed in the Related_Case__c field. After the deletion, all records can be re-added into the object like new. If I went this route, I would update the auto text Name value on the CC_List__c object to text with a single dummy value as you have originally shown in order to avoid confusion.

Thoughts?