I know how you are feeling. I hunt deer and rabbits but could never put down my own dog. I have gotten a local hunter to do it before. One shot to the head, and he even wrapped her in a blanket for me so I could bury her myself but didn't have to see her.
I wouldn't recommend poisoning, could be long and painful.
Try asking someone at a hunting club nearby. Most hunting men will "come to the rescue" in situations like this. I hate to say it but this is one area where stereotypes and gender roles helps a lot.
Sorry about your baby.
*EDIT* Also, it seems like a lot of people here didn't grow up in the country. Shooting an animal is a normal thing. For food, and in situations like this. Also, out there you don't have unlimited resources. Our closest vet was about an hour away, and they were mobile for large animals but it did cost about $800.00 to have our horse put down when it was time. That cost is the same regardless of size. An emergency with our pets usually meant calling the vet and handling it yourself. I learned to sew up and sterilize wounds when I was young. Also, birthing pets, when someone dropped a pregnant stray 'in the country'. The only vet visits are for spaying and castrating, or for a few other rare occurences.