You did what was right for her even though it was hard on you.
I've stayed with all my pets from cats to horses who had to be euthanized, I felt I owed them that last bit of familiarity.
If I could have reliably ended their suffering as you described I would have done so gladly.
No need to involve a vet if you have the means.
For the larger animals having a vet administer is safest, as reaction to the drug can be dangerous even if sedation is given first.
If I were a marksman (I have zero firearm knowledge) a well-placed shot can be quick and painless.