ggirl, i used to be a veterinary nurse and have assisted in putting many dogs and cats to sleep, including my own.
You have raised two issues here which i can adress. Firstly, you said you want your dog to die, feeling safe and knowing that you love her. Well, to garuntee this then i think putting her to sleep is the best option, for this reason: You can be with her, you can hold her and cuddle her. They simply give the dog an overdose on anaesthetic and they just go off to sleep. They do not tend to bother to shave the leg to be honest, at least we don't, providing there is an easily accessible vein. The thing is, you don't want to leave it until she is so poorly that her blood pressure drops as this can make getting a vein difficult, but still minimum discomfort to the animal.
Definately insist on a home visit, most practices offer this, if yours doesnt ask them to recommend a vet that does, they wont mind.
You don't say what is wrong with her. Is it that she is just old and knackered and the bowels becoming a problem? If she is losing control of her bowls, this will be upsetting for her and it becomes an issue of letting her go with dignity. If you have to wait for nature to take its course, yes, she may well drift off in her sleep, but she might not and it could be scary and uncomfortable for her, if you chose to put her to sleep you can ensure that she has a peaceful end.
I have had to advise many sad and upset owners facing the difficult decision to put their animals to sleep. What i say to them is this - go with your stomach. Your heart will talk you out of it and your head will try and rationalise yourself out of it with things like, well she had a good day yesterday etc. But in your stomach, you'll know.
I'm very sorry about your pet - she is lucky to have such a caring and concerned owner and im sure you will make the right decision for you all.