I'm sure it's an awful thing when a beloved pet becomes ill, especially chronically ill. I watched my friend John go through this when his Dalmatian, Amadeus, who was about Coco's age, developed, er, incurable bladder problems. It was sad for John and sad for Amadeus.
Based on my observations of his experience, I can sympathize with you and your mother, Lee, but, again based on my observation, there are difficult questions to be addressed here. This isn't just a matter of your mother giving Coco a shot twice a day.
Can Coco's vet offer any guidance as to what her life expectancy is now? What about her quality of life? What kind of an emotional burden would it be on your mother to administer the injections twice a day--or can you stop by twice a day and give Coco her shots? And what kind of a financial burden would this place on your mother if she has to pay for twice-daily insulin for Coco for an indefinite period?
Or can you take Coco into your home and care for her?