Actually, eastern coyotes are much bigger than western ones. But llamas, which weigh 500 pounds and up, can certainly stomp a coyote that weighs one-tenth of that. I don’t know why they are so aggressive, but when they see a predator they go nuts.
There’s a video somewhere of a donkey attacking and killing a cougar. It’s amazing. You start to feel sorry for the cougar.
Mule Kills Mountain Lion
"These pics came from a guy in Arizona. Yes, the mule killed the mountain lion. The lion had been stalking them for the better part of the morning, on the way out to a hunt. They were pretty sure it was after one of the dogs. The cat ambushed them, and the mule pictured tossed its rider and went into attack (defense) mode, the horses scattered and shots were fired but no one was sure if they hit the cat or not. Unfortunately, it wasn't until it was almost over that one of the guys started snapping pics. The mule finally stomped the cougar to death after biting and throwing it around like a rag doll. The dogs wouldn't even come close until the mule settled down.
The cat was still alive here and trying to fight back
The mule stomped the cat then pinned it to the ground and bit the heck out of the dead cat several more times.
The cat was pretty much dead by now then mule picked up the cat again whipped it into the air again then stomped the dead cat again for good measure!
Llamas are very protective, but coyotes generally don’t let donks and llamas get near them. Heck, I’ve seen steers chase coyotes out of pastures. Coyotes are oportunistic hunters and seldom risk getting injured...they test and if anything responds aggresively they generally back off.
I did not see the video you mention but for awhile there were a series of digital photos of a mule and a cougar, and alas, like much on the internet, the photos were later proven to be staged. The cougar was already dead and some interprising guides had rigged the whole thing.
I have quite a bit of experience with yippee dogs...I now live in rural Idaho but have worked all over the west including a few years cowboying in central Nevada. I hear the little buggars every night where I’m living now. I normally let them do their thing until calving season; then I will plink at them and they normally back off. Again, about the first time you shoot at one, your next shot will be at a pretty long distance.