William,
Sorry to hear about Lucy. I understand you have to think of your family first. Do you think they will let you be with her when they put her to sleep? The vet usually lets you be your pet when they have to be put down due to old age or severe illness. That way she may be comforted by your presence during her last moments and at least you would have some peace knowing that you did as much as you could for her.
It's hard losing a pet regardless of the manner in which they go.
Phillip,
Your story about Bonnie had me in tears. Ditto on your comment "please don't stay away, you will want to remember your Pup happy to see you, not wondering where you are. Yes you will feel remorse for having to do it, but know this, you know that he/she went with you in his mind, not feeling abandonded and unwanted."