Oh Wildcard,
I am so very sorry for you, your wife and your daughter and little Max too. I really believe animals have souls and I believe Max is up in heaven right now, running around as happy as can be. When you have a pet, you realize they have enotions, they love and learn just like humans. That is why I believe they have souls and are not just "dumb animals". It is going to take you all a while--it took me five weeks with my last cat, then one day I woke up and
thought, "it isn't so bad now". My own vet has lost several dogs and he says the first three weeks are really bad, so you guys just hang in there and be easy with yourselves. Try to be extra kind with each other, expecially your dayghter.
I am glad you were with him at the end to comfort him. The best way to look at it is that you had Max to enjoy for a long time. Sending you three a big hug and my deepest condolences.