My condolences - that seems like a lot of family for that short length of time.
When I used the word "tradition" it wasn't so much as an ethnic, cultural or religious tradition but the practice of people in public life, or rather those where public funerals seem reasonable or expected whether they're royalty, a world leader (or their spouse like Nancy Reagan), politicians or a fallen police officer or firefighter. In these cases, the trend always seems to be to have a casket present. Not "keeping score" or anything, I just can't recall ever not seeing a casket. In my little world of non-public life with good but mostly ordinary people it seems odd. Not to sound glib but I guess the casket facilitates the draping of a flag because what would you do otherwise?