How do you handle euthanasias and the aftermath?

I'm a current 4th year student and we euthanized one of my patients today. The dog basically couldn't breathe outside of an oxygen cage and was bleeding out into the lungs. There wasn't much we could have done with this dog since it was very likely it had horrible mets to the lungs (diffuse milliary pattern) and there aren't many treatment options we could do given the oxygen dependency. I listened to these owners wrestle back and forth on what to do and ultimately they wanted the dog to go home and be euthanized. However they lived 4+ hours away and we had no way of transporting the dog with oxygen on such short notice. They finally euthanized at the hospital when it was obvious the dog wasn't going to survive much longer even in the oxygen cage.

I watched an entire family bawl as the dog slipped away. The teenage kid that was stoic during the whole few hours prior was uncontrollably sobbing during the euthanasia. The mom wanted to just hold the dog afterwards. I almost broke out into tears multiple times feeling the pain of this family losing one of their own. The residents I was working with were so put together during the whole thing. I guess they have seen this way more than I have, though this was not my first euthanasia. It just hit me harder today than other days. They kept asking us if they did right by their dog. I had a hard time writing the sympathy card because I didn't know what to say because nothing I say would make it better.

I know the career ahead of me holds a lot more experiences like this and I always knew it would be hard. I'm sure the more I go through them the more these answers will come to me. However, I'm hoping to get any advice on how the vet reddit community handles euthanasias and what you do to try to make things better for your clients, patients and also yourselves in the aftermath.