time to euthanize?

My elderly parents had a dog, Sherlock which i have had for the last 2 years. My dad passed away 2 years ago and Sherlock would wander the house looking for him. Shortly after, my mom began falling, sometimes with serious injuries. She moved into an assisted living apartment and is unable to have the dog there mainly because she is unable to take him out to potty, feed him, etc... He's been depressed at my house, though i've tried to be good to him. He hasn't eaten as well and has lost a lot of weight. His normal weight when he lived with my parents was about 24 pounds. I've taken him every 6 months for a checkup and each time the weight is down. The vet says each time that it'd be better for him to weigh more, he's a little too thin, but nothing to be too worried over. These last 2 months, however, he's declined very rapidly. He never barks anymore, he paces aimlessly when he's not sleeping. I have to sit with him and coax him to eat, have tried every food you can think of - name brands, store brands, canned (chunky varieties as well as "mush" varieties), semi-moist, dry, prescription food, senior diet, you name it. He'll eat the semi-moist if i coax, but even then i can only get him to eat about a half packet a day. Had him to the vet 6 weeks ago, and his bloodwork is all normal, the vet can't find anything wrong in terms of a disease or anything to explain the lethargy. "healthy" He's lost bowel and bladder control and, while i feel like a bad person for doing it, i've started keeping him outside in desparation. He poops and pees and walks through it back and forth as he wanders and within a short time he has it tracked throughout the house. I literally spent 50 minutes one morning scrubbing the floors trying to get it all cleaned. I tried kenneling and he makes a mess in the kennel with feces in his fur, his ear where he laid in it. I tried confining him to a small area but then the mess is really just in the small area. My house is fairly open so the only areas i can block off that aren't carpeted are the laundry room (pee runs under the washer and dryer, that's a problem) and a short hallway which is my only way out of my bedroom. the mess is so bad sometimes i literally can't get out of my bedroom to clean up the mess without walking through it myself. So, it's outside. I live in Texas and it's already hitting 100, way too hot for this dog given his age and given that he's been an indoor dog all his life. After agonizing what to do for Sherlock, I came to the conclusion that he's so unhappy, doesn't do anything he used to enjoy, is isolated and suffering. I took him to the vet last night with a clear request to have him euthanized. The vet looked at his charts and concluded that he has no medical reason to euthanize and cannot do so in good conscience. this dog weighed in at 14.8 pounds last night, i see his backbone and his hip bones. The vet gave me Tramadol for him, saying that maybe he'd eat better with the pain meds. I can't get the Tramadol down him, have tried hiding it in food (that's a circular problem, I got him to take a bit of wet food but as soon as he tased the pain pill, out it came). I put one in one of those pocket treats, i can't even get Sherlock to take the treat. I tried putting it down his throat. i've owned dogs all my life and have done this wtih a half dozen dogs many times. but there's no way i can do it with Sherlock. This is the one time i see a spark of life, the struggle is surprising and he's bitten me a couple of times in my attempts. So, sorry for the very long post - am i wrong to think it's time to let this old guy go peacefully and with dignity? The vet has me feeling as though i made the request for my own convenience. yes, the dog is outside as a "convenience" i don't think it's sanitary to have feces and urine daily spread around the house. but, the refusal to eat, the weight loss, the aimless wandering, no barking (what daschund doesn't bark at things?), did i mention his hearing and sight are really bad now. i think this dog has no will to live and is miserable. Yes, an elderly dog loses some mobility and spark, but this dog is just a shadow of his former self.