Well, disputes occur between members within all social species. Interaction — which is what being social is about — involves and runs the gamut from simple communication, to camaraderie, play, friendship, and agreement, to disagreement, oneupmanship, disputes, fights, and becoming enemies. It happens in human families, and it happens within families of other social species as well, and here it happens between coyotes.
I put out a field camera next to picnic tables a few nights ago. I’ve put it out here before — it’s a good spot because animals regularly come by — mostly raccoons and a skunk. The camera amazingly captured an intense fight between the alpha male and alpha female of a coyote family I’m following: yikes, a family fight! In the video, it’s the alpha male who charges in and angrily confronts the female. She stands up for herself and fights back angrily. Make sure to have your audio on, as the sounds are impressive. These are mature coyotes who only recently have become a pair in a sort of reconfigured family. Each had been part of different families before their changed circumstances (for instance, death of one of their mates) caused them to come together. It could be that the fight in this video is them still working out the hierarchy between themselves. Then again, maybe it’s just a little squabble, or something bigger going on. I don’t know.
When coyotes communicate, be it to our dogs or each other, they are intense about it so that there is no uncertainty, misinterpretation or misunderstanding about what they are trying to get across. Here is a video of a mother coyote communicating to a dog in no uncertain terms: it is intense, insistent and persistent which sometimes makes it very scary to us civilized humans. And here is a photo of a snarly communication by an older sibling to a youngster: notice the surley face, angry eyes, wrinkled nose, gaping mouth, and teeth showing, and this occurred right after the youngster had extended a very warm greeting to that older brother. As I say, coyote communication is intense. This, along with deep growling or grunting is how they communicate with each other, and if that doesn’t work, they can get physical, as in this video.
Coyote Yipps 
Sep 24, 2021 @ 17:41:11
As someone who owns native stock Basenjis, when I watched your video, I saw no intent to injure. In fact, as with my primitive breed, when there is intent to harm, interactions are typically silent or very quiet. Vocalizations are basically bluster, like chest beating in gorillas To the inexperienced dog owner who is new to the Basenji breed, it can be terrifying. But I don’t know any long-term Basenji owner (multiples in the home at the same time) who would watch your video and be concerned or alarmed. Thank you for sharing!
Sep 24, 2021 @ 18:52:23
Hi Jo —
I absolutely agree: this was a communication — an angry one, at that, but just a communication. There was snarling, but no biting, or as you said, no intent to injure. And the vocalizations are part of that communication: in this case a display of anger, and possibly a warning of some kind. Thank you, Jo, for your input! :))
Sep 25, 2021 @ 01:34:00
Fascinating behavior. Was the mother coyote— in the dog-coyote interaction—caught in a wire fence? Coyotes are much better at communicating their disagreements than most humans…
Sep 25, 2021 @ 02:11:47
I’m not sure exactly what you mean: neither dog nor coyote were “caught in a wire fence”, but this was a fenced-off-to-dogs enclosed property.
Sep 25, 2021 @ 02:46:03
I thought there was a wire fence in the foreground that she kept getting her feet stuck in. Thinking it’s time for new glasses 🤣😂
Sep 25, 2021 @ 04:25:48
No, just overgrown brambles and branches!! :))