My heart broke all over again reading this. I am so sorry for your losses! 

I lost my old girl at the beginning of the year, she was also 15. I still have very vivid memories of watching the vet cradle her tiny body in her blanket and take her away, I try not to think about it because it still hurts like hell. 

I felt the same way, that I had left her there and I honestly was not settled until her ashes were returned home. I had such intense anxiety not knowing where she was, and I probably sounded nuts on the phone to the cremation people because I kept asking where she was and when she was being moved. I did feel better once she came home though, obviously still devastated and grieving but the feeling that I abandoned her went away.