If your vet wants to do a C-section without even waiting to see if the goat can deliver, find another vet. Repositioning kids is not hard (3 or 4 are more difficult, but doable). You just to have to get inside, sort out the body parts and pull them out. I played a game with my 4-H project kids where we put a bunch of stuffed animals in a pillow case so it was stuffed and the kids had to identify what they were feeling.
When I go inside a doe or ewe to reposition and sort out babies, I always feel like that scene in Men in Black when the hero gets swallowed by the giant cockroach alien! Just as slimy, but necessary. Go slow, and ease in with lots of antiseptic soap or special birthing lube if you have it. Make sure you feel any legs or body portions all the way up to the body so you know what they are and that they belong to the same baby.
I always close my eyes so I can let my hands tell my mind what part I am feeling when I go inside. Mu project kids used to call me to help if their animals had trouble. (My neighbor even had me come pull her colt.) One time I went to help pull kids from a doe that was in trouble. One was stillborn and she still had a kid inside - I could feel the head and bones when I picked up her belly. I told the family that the other kid might be dead too, but I would pull it to save the doe I greased up with antiseptic soap, closed my eyes and went inside the doe. She was terribly tight which was odd, it felt like the cervix had already closed up. If the kid was dead for some time, maybe the doe's body was telling her everything was over, but I had felt a kid inside when I palpated so I kept trying to find it. Nothing, but tightness. As the familyheld their breaths in worry, I opened my eyes and realized I was inside the rectum!!!
OOPS!!!
I quickly pulled my hand out, scrubbed off, resoaped and this time found, repositioned, and pulled a live kid from the correct opening. It just shows that even the most experienced can make mistakes. That is one of the jokes I love telling on myself!
Southern: If you want to do posting about repositioning and pulling kids and lambs, let me know and I will contribute.