It's not in every household that dogs live in harmony. Dogs who lack socialization skills or aren't corrected during their young age when they become aggressive can turn dangerous.
A couple of days ago, my shih tzu decided to pick a fight with a bigger dog. The bigger dog was nice enough to put up with him but eventually the constant growling and biting from the shih tzu got to him.
I sprayed them with a water hose but the shih tzu still came after the bigger dog who already backed down. You'd imagine how that turned out to be.
Armed with nothing else and without anyone I could have asked help from, I grabbed each dog on the back of their neck, separated them and had them lie down on their side until their body started relaxing. (It's important to be cautious-but not hesitant- in doing this because there's a big possibility that you might get bitten yourself.)
What would you do to stop two dogs from fighting?
In the short term I'd do pretty much as you did - try to seprate them by whateer means possible. In the medium term I'd get them spayed or neutered if they aren't already.
But in the long term I'd got to a dog training school this will really help any dog to socialise with other dogs, and humans, and to learn how to find it's place in the pack that it happens to be in at any given time.
I have 2 dogs - both from a rescue centre who's package included 2 lessons with a dog trainer. I continued (it was fun as well) to complete a course of 10 lessons.
I haven't had to worry about this too often. In the cases where it's happened, I haven't been near a hose or anything like that. What I've done is I've used my voice.
I'm not a big person at 4 ft. 10 inches, so it's not likely I will scare many. But, I was born with a deep, strong voice. The dog trainer I had with my Lab taught me that you can use your voice in such a way to startle the dogs, so they stop fighting.
I have to admit that I've only had to test this out on dogs I know. Though, I have used my voice to scare of stray dogs in my neighborhood. My Lab got into a fight with my sister's German Shepherd mix over the treat ball years ago. I charged them while yelling a certain way and they stopped. Of course, the German Shepherd was somewhat terrified of me the rest of the night.
I've had to do the same thing more recently with my sister's dog and my brother's Chow mix. Both are good dogs and get along 95% of the time. It's the 5% when there is food around that things happen. I've been able to break up those fights with my voice as well.
That is the immediate action. In the long term, training is necessary. For instance, I've noticed my Jack Russell can be a bit food possessive. I've been working with her on this because from time to time my sister's dog stays with me. Luckily, their incidences have only been Misha growling and the big dog walking away. But, I realize that this could escalate and Misha would lose.
What I've done is I've worked with her at her bowl. She must sit and wait for her meals. I've worked with her on her "leave it" command when I give her treats. When my sister's dog is here, they each get two Cheerios at breakfast time. Misha must wait for Summit to eat hers. She must not steal it like she will try to do.
I can say after many months of working with her that she is doing much better. She will actually stand patiently for those Cheerios. She will also wait for treats. She shows Summit a lot more respect now.
I do have to separate them at meal time. It's because Summit gets special seizure medication on her food. I can't risk Misha getting into it. But, also, Summit is a very slow eater and easily distracted. She won't eat if Misha is running around.
So, I'd say there are two things you have to do. You have to be able to take some sort of immediate action that is effective. Then, you must work on the behaviors that might be causing the dogs to fight in the first place.