I'm so sorry for your loss. A couple years ago, just after Christmas we had to have my Mom's dog, Buck, put to sleep due to a hemangiosarcoma. I was visiting and noted that something was wrong; he'd stand up, take a few steps, then collapse and pant. When we got him to the animal hospital's 24-hour emergency care center over in Louisville, they did tests and told us that the cancer had ruptured his spleen and that the reason he was so weak was that he didn't have enough blood circulating to carry oxygen. They ran blood tests and said it had spread to his liver, and was terminal. He was unlikely to survive surgery and if he did, he wouldn't live long enough to recover from it.
We cried and decided to have him euthanized -- then we sat with him as he went under. I still mourn his loss even though he wasn't my dog. Insensitive people have told me, "It's only a dog." They don't understand how big a part of our lives a pet can be. So, I know exactly what you're talking about and going through. It's OK to mourn, even though some people won't understand; Sallie will hold a permanent place in your heart as a beloved lost companion and family member, and that's OK too.