My criteria for when it's "time" is
Pain, if they have trouble standing up, or walking, or cry out and a daily pill is not working to keep them comfortable.
Incontinence. If they start dribbling from any orificie when they walk, they are "done" around here.
Sleeping almost all the time
Tumors that are large an inoperable and cause problems,
Any really expensive vet problem very late in life is a deal breaker for me. I just don't have the $ to treat a very old dog.
If you parents are not wanting to buy the dog food, maybe you could offer to pay for it. It would show how much you care about your dog, which, by the way, looks fine to me in the pic. Bright expression, good coat, not obese. You have done a great job with that dog for her to live as long as she had and stayed so healthy. The breeder too gets big props in my book. Just thank heaven you had what you had with that dog. You have been very fortunate to have such a great dog live so long.