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What’s the best way to break up a dog fight at the dog park?
You got it in one.
If you can't use non contact methods, you grab their back legs and pull them apart. Takes one person per dog, which isn't perfect, but it's the safest hands-on way.
If there's no other choice, you can try naping one or both, but the truth is that if they have any size at all, it won't work, and it's way more likely for everyone involved to take injury. But if it's life or death, it could work, as long as you have enough strength to do it. Just be prepared to get bit, and for any of the dogs involved to potentially be injured; adult dogs don't do well being hauled around by the back of their necks, even (maybe especially) the little ones.
I'd make sure to take a startle can and a decent sized blanket with you. Startling them ata park is likely to fail, but it's easier than trying to get them covered enough to get them snapped out of the fight. Most dogs though, you throw a blanket on them, and it switches their brain to a different state. It's part surprise, part the decrease in light. Doesn't always work, but it's likely to work better than grabbing their legs at stopping the mental state that caused the fight.
That's the real difficulty; if the dogs are still locked into fight mode, it's going to take longer to really stop it. Not that a cover is perfect in that regard, just better. It's the old saw about how if you control the nose, you control the head, and if you control the head, you control the dog. Just with eyes instead of nose, which is one of the rare instances where that works. They go from focused fully to having to adjust to not being able to see, and the rest of their brain has to adjust too, so the fight gets forgotten.