I believe cancer is very common in dogs, unfortunately. And in my opinion, I truly question how much diet plays a role in it. Audubon was on one of the expensive "better" diets that are pushed often, and she ended up with a mast cell tumor at only 6 years old.
Jake has a tumor on his chest, but it is non-cancerous, and cannot be removed because of his heart.
My mom's 17y/o dachshund has breast cancer, her 16 year old dachshund that died last year had breast cancer. My brothers two (2!!!) year old chihuahua has mammary cancer, my foster dachshund that is only 2 years (!!) old has breast cancer. A mix breed terrier that I had when I was younger, died 1 month after his 10th birthday from a very aggressive form of anal cancer. He died 3 weeks after the diagnosis, and it had already spread to all of his organs.
I could go on and on about my mom's dogs, my friend's dogs, my relatives dogs, all died or have had and been treated for, cancer. My vet raises standard poodles, and almost every poodle he has ever lost, he lost to cancer. Only one didn't die from cancer, she got hit by a car several years ago.
When I worked at my vet, we had a 18 month old border collie mix die from mast cell cancer, and he was fed a grain free diet. A friend of ours lost their 6 year old lab mix to cancer, and she was fed a raw diet her whole life. A friend of our family lost his 8 year old border collie mix to cancer, and she was fed a home-cooked diet.
Really, I think cancer is the result of a lot of things, not *just* diet. Environmental pollutants, genes, over vaccination, overabuandance of chemicals (putting on flea products every month for years and years), ect. And, sadly, it's also just a fact of life.
My uncle has been a marathon runner since his teenager years, and he's now 70. Never ate fast food a day in his life (he loves to tell people that too, how he survived his life without McD's, LOL), never smoked, never drank, and very active in athletics until this very day. He ate the healthiest diet of fresh fruits and vegetables, no overabundance of red meats and no greasy or unhealthy foods. And he never took medication, not even tylenol. If anything, he's the model of someone who would never get cancer. Guess what? He was just recently diagnosed with cancer.
So I give up trying to figure out what causes it. *Shrugs*
Sorry to hear about your family's dog though.