[SalesForce] How to evaluate multiple child records in order to update a parent’s status

I have a sample request (header) table and product information (details).
What I'm trying to do is after a product is shipped, an integration writes to the child record(s) and updates a field called: ship date actual with a date for when the product has been shipped. After all the child records have been marked with a ship date- the system should then update the parent status to Shipped. Otherwise, if there are child records not yet marked with a ship date- then keep the header status as it is: approved. I'm new to this- (I know, terribly obvious).

Parent Table: Sample_Request_Account_Information__c

Child Table:
Sample_Request_Product_Information__c

Here is my apex code: I tried to look at an example which was posted on this forum to try my best to get this to work:

Apex Class:
/** Updates the status field on Sample Request Account Information*/

public with sharing class childTriggerHandler {
   public void UpdateFields(List< Sample_Request_Product_Information__c > newList) 
   {
        List< Sample_Request_Account_Information__c > updateList = new List< Sample_Request_Account_Information__c >();
        Map<id,List< Sample_Request_Product_Information__c >> mapParentIDAndChild = new Map<id,List< Sample_Request_Product_Information__c >>();
        boolean flag;
        set<Id> parentTrue = new set<Id>();
        for(Sample_Request_Product_Information__c objChild : newList) {
            parentTrue.add(objChild.(Sample_Request_Account_Information__c));
        }
        for(Sample_Request_Product_Information__c objChild : [select id , Ship_Date_Actual__c, Sample_Request_Account_Information__c from Sample_Request_Product_Information__c where Sample_Request_Account_Information__c IN: parentTrue] ){
            system.debug('<<<<<<objChild '+objChild );
            if(mapParentIDAndChild.containsKey(objChild.Sample_Request_Account_Information__c)) {
                system.debug('<<<<<<in if 1st ');
                mapParentIDAndChild.get(objChild.(Sample_Request_Account_Information__c).add(objChild));
                system.debug('<<<<<<in if 1st mapParentIDAndChild '+mapParentIDAndChild);
            } else {
                system.debug('<<<<<<in else 1st ');
                mapParentIDAndChild.put(objChild.Sample_Request_Account_Information__c,new List< Sample_Request_Product_Information__c >{objChild});
                system.debug('<<<<<<in else 1st mapParentIDAndChild '+mapParentIDAndChild);
            }
        }
        for(Id objId : mapParentIDAndChild.keySet()) {
            flag = true;
            for(Sample_Request_Product_Information__c objChild : mapParentIDAndChild.get(objId)) {
                if(objChild.Ship_Date_Actual__c !==''){
                    flag = true;
                    break;
                }
            }
            if(flag == true) {
                updateList.add(new Sample_Request_Account_Information__c (Id = objId , Status__c = 'Shipped'));
            } else {
                updateList.add(new Sample_Request_Account_Information__c (Id = objId , Status__c = 'Approved'));
            }
        }
        if(!updateList.isEmpty()) {
            update updateList;
        }
    }// end of UpdateFields
}// end of childTriggerHandler