I have, unfortunately, been in this spot several times over the years. Each time I tried my best to put my personal feelings aside and focus on what was best for the animal in the long run. That is really all anyone can do. Then, no matter which way it finally goes, you know deep in your gut that you did the right thing, whatever that thing turns out to be. Unfortunately that doesn't make the decision easier. But later it does give you something to hold onto in the wee hours.
My heart goes out to you both.
H