That is beside the point.
This is not your dog's fault, it's not your kid's fault, and it's not your neighbor's fault. It is your fault for not training your dog better. An aggressive great dane is absolutely unacceptable in a residential area. You should have socialized him since he was a puppy, with the understanding that if he grew up with an aggressive temperament that something like this would likely happen.
I'm not trying to be a dick, but if you want to avoid something like this in the future then you need to recognize what you did wrong in the first place.
Sorry for your loss.
This.
I am aware this might feel like rubbing salt in fresh wound, but this tragedy was completely avoidable. And unfortunately, as the responsible adult in the picture, you take most of the blame.
Great Danes are huge dogs, not to be adopted lightly. They need to be very well trained. At the same time, they are very friendly - they love being with other animals, kids and people in general. The fact that Trooper was not so, speaks to his training, or lack thereof. The very first time he bit somebody, should have been your warning to step in, recognize the problem and correct it. Good training at even that stage might have fixed it. But looking at your post it's very clear you have been (and still are) in denial : the lady pet him
without permission, the mailman
leaned into the house. No, the fault was not with them, particularly looking at the breed of the dog. (And I mean the real fault : please don't split hairs here about each circumstance).
I hope you take this in the right spirit : if you get another dog, know the breed, know your responsibilities. Even rottweilers can be loveable with the right environment, and Great Danes are actually cuddly compared to Rotts.
<Now the universe is going to chomp me in the butt today for berating somebody in mourning...aah well>