I'm so sorry, and so sorry your vet has upset you, it was very insensitive of them to speak in that way.

A competent vet should be able to find a vein without causing any distress, and the euthanasia meds work very quickly and peacefully. Talk to your vet and explain your anxieties, they really should understand how you feel.
I think they sometimes try to discuss arrangements before hand as it would seem even more callous to discuss it immediately afterwards, but they could have taken more notice of your feelings and done it in a more caring manner.

The idea of someone coming to your house sounds like a good one to consider, as you would have a little more control over the surroundings and hopefully feel less stressed .

It never gets easier to lose an animal you love so much, but my life would be so empty without them.

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