Wow.. this is such a hard question since this really hits home.
A few years ago, my wife and I had the decision to make of .. well, putting her guide dog down, or keeping her and letting what was happening naturally happen. What made it hard for us was that her dog just wasn't part of our family; she was my wife's eyes, and if it weren't for Willa, my wife and I wouldn't have met (that's another fun story for another time).
Long story short, a few years after we retired her, we found out she had cancer, and needed to figure out what we were going to do. it was affecting her ability to walk, eat, let alone enjoy her life of just being a normal dog. So eventually we came to the decision that it was time.
I've lost pets before, at times when a kid should never have to learn about death so early in life, but I have to tell you that letting Willa go was the second hardest thing I've ever had to go through in my life (believe me, you don't want to know the 1st). We took her to the vet, who set up our own private room so we could be with her, and we stayed as long as they could let us, even after it happened. And call me a sook, wimp, what have you (I'll wear that with pride), but I was an absolute crying sobbing mess when we left. We both were.
After getting ourselves cleaned up, the only way we could think of to get us out of that funk, was to be with those who understood the plight; so we went to our friend's house, who is a Guide dog Puppy Raiser. You'd think that visiting them and playing with the puppies that would become service animals would be insult to injury, but it really helped, because we needed that.
Without our knowing, that vet not only stopped by and delivered Willa back to us (we asked for cremation), but they also made a $1500 donation to our local university's veterinary program, as well as a donation to Guide dogs for the Blind, in our name.
Now, every day, we look up on our bookshelf, and see Willa, with her collar and guide dog tags around her as she watches over us.
I guess my point with all of this is that you should choose what helps you to heal but never forget them, as they are part of you. They aren't just a pet that you can replace; they're family. Treat them like such, and don't ever, ever forget them.
BL.