Your post broke my heart. I cannot begin to tell you how dreadfully sorry I am about the horrible position you were put it. Please accept my deepest sympathy and condolences.
You did the right thing and I do not say that lightly because I love dogs with all my heart--IF I know that I can trust them.
When I was a child I was viciously attacked and bitten by a pack of loose dogs. If my father and his friend had not gotten to us in time my poor sister and I would have been ripped to pieces and killed. I have carried the physical and emotional scars of that horrendously terrifying attack to this day and my entire life since then has been seriously impacted even though it happened over 50 years ago.
To make matters even worse was the fact that we learned that my sister and I weren't their first victims--the dogs had attacked before and had killed two people in another state. The owner knew that they were dangerous and he should have put them down but he didn't. Instead he fled the state with them and moved out here to hide. He thought that he could keep the dogs safely contained but they got loose--accidents happen!--and my sister and I paid the price. The dogs did too--my father went back and shot all of the dogs.
It sounds like your dogs behavior was escalating dangerously. If he was that aggressive towards people at two how do you think he would be in another year? Not only would he have been very difficult--if not impossible-- to rehome but knowing how dangerous he was becoming would you be able to sleep at night if he was rehomed knowing that a "ticking time bomb" was out there and that if he attacked someone in the future that it would be YOUR fault for not doing what you knew had to be done? Also what type of person would knowingly adopt a dangerous big German Shepherd that could not be trusted? Maybe you would be lucky enough to find that one in a million who was a decent person who would take him (but what if he attacked the new owner or one of their family members or got loose and attacked someone?) but chances are he would have wound up in the hands of a real creep and you should shudder to even think about what kind of a life he would have had.
And because of your son keeping him was NOT an option. What do you think you could do? Keep him locked up in a room (he was a big German Shepherd not a tiny Chihuahua) 24 hours a day and only take him out for a walk? If he was that aggressive at the vets do you honestly think that it wasn't just a matter of time until walking him put others in danger? Or how about making him live locked up all alone in a pen in the yard 24 hours a day if you have a yard? Do you think that would be a nice thing to do to him? He would be miserable and you would be his jailer. And if you think that somehow you could always keep him safely contained outside or locked up in a room 24 hours a day 365 days a year for the next 12 to 15 years don't fool yourself--ACCIDENTS HAPPEN!
You made the only responsible decision that you could have made under the circumstances. But because you loved so much him it hurts you horribly and I am so terribly sorry for the awful position that you were put in and the horrendous pain and grief it caused you.
Please try to take some comfort in the fact that your beloved dog is now in Heaven. I'm a Born Again Christian and the Bible teaches that ALL animals--unlike all people--go there. Your dog is running free and playing and leaping for joy in the gorgeous green fields of Heaven. If you are not sure if the Bible is true or not here is an excellent link that proves beyond a shadow of a doubt that it is and offers two ways to read the free book
Once again I am so terribly, terribly sorry.