My mom's dog was diagnosed with terminal cancer 5 years ago but she has made it to age 12. However she now has three tumors and really bad hip dysphasia. My question is if we decide to put the dog down will it make my moms Alzheimer's worse? She dotes on and loves the dog. I don't want to make my mom worse.
As long as dog is eating and "bodily functions" are working - other issues especially so long after diagnosis don't matter so much.
If dog goes, and if you can handle taking care of another - please consider adopting an older dog (rescues, and animal shelter have lots and lots)
A dog offers non-judgmental support and love. If you can help to take care of it, it may keep Mom happier. Not to mention helping to save the life of an "unwanted" dog.
Otherwise, if the pet is happy and doing fine, even with the tumors and hip dysphasia, the dog could enjoy another year or two, and your Mom could continue to enjoy her pet.