We have opportunity as parent object and this parent object has several related list(lookup or masterdetail), whenever the fields in the child object is changed this should update the opportunity last modified custom field.
Ok, simplest option, i.e. no code, is a Process on each child object, fired when created or updated, Opportunity__c (lookup or master) is not null, update related object (Opportunity__c>>Custom_Last_Modified__c.
This would update the field on Opportunity each time one of the records is updated.
Other option is an Apex helper class and a trigger on each object to call the class, passing in the sObject variables.
I'd go for option 1 for a future perspective.