You and Annie are in our prayers.
We have been through similar situations several times, and have prayed the same way and asked the same questions.
The determining factor was whether our beloved companions were in pain. The ones that were not died peacefully in our arms at home with the other animals also near by. The ones that were in pain, and that the vet couldn't do anything to help, we decided the most loving and compassionate thing to do was to put them to sleep, and they also died very peaceably in our arms.
In all these cases, we felt a deep loss, but were at peace that we did the correct thing.
In the Love of the Lord,
Frank and Mary