Big hugs to you all. A horrible situation for you, and I can't imagine how I would cope.
I have had 2 ponies pts (both times by the vet - one was buried on the farm as we had a JCB here anyway, the other was collected for disposal the next morning - all very sympathetically handled. Both times by injection - they were elderly rescue ponies - quick and peaceful, other ponies in attendance).
I wanted to be myself, but you may prefer to have a friend or family member with you. It took a few days before I could speak to anyone apart from hubby, but now I can smile and remember all the good times.
It is definitely the bravest thing we can do for our beloved animals - the pain is over.
Ali xx