I am sorry Lisalisa. Grief is a painful thing and I guess you have both grief and shock to cope with here.
But you don't have to rush into anything. You can adjust slowly and let the whole family get used to the idea, perhaps decide if a few little rituals would help.
Anyway, as to the practicalities (so don't read this bit until you are ready) it's so straightforward. Literally one small injection in the loose skin of the neck and the heart stops pretty much instantaneously. I vividly remember my mother giving one of her dogs a bit of sausage to chew on while the vet gave him the injection and he dropped down dead mid chew. Didn't know anything about it at all.
Do you think it might be less stressful if you could get the vet to come to you? I don't know if vets still do housecalls for this sort of thing.