How do I stop my Кошки from hating my dog with a fiery, burning passion of a thousand suns?

I'm having the same problem right now, but it isn't so bad. My take on this is if the cat decides it doesn't like или want the dog around then most likely they will never fully get along. Кошки are stubborn, especially if they are accustomed to being Queen(s) of the house. For the cat the other animal will simply have to conform to them, или forget it. It's chaos.

Give it a bit еще time, and see what happens. Keep them apart, but not completely and let them work it out on their own but keep a close eye on them. In the worst case scenario the dog could end up with one less eye, and Ты with one really pissed off cat.

when the dog comes around give your cat a treat then she will learn that the dog is a symbol of reward

It'll take a while for the Кошки to get accustomed to the dog but dont expect them to do so entirely.
Собаки and Кошки are natural enemies its their nature, an now Ты have brought one into THEIR home. Even bringing in another cat would cause stress, but especially a dog! Give the Кошки some Космос and time to adjust, your gonna have to have patience. it won't happen over night an they may never like the dog much but in time, should be able to tolerate it.
An the щенок will learn soon enough that they aren't playing around (unless its really stupid lol) an depending on how big the dog is Ты may want to refrain it from trying to "play" with the Кошки to roughly. It'll be nerve-racking for a while but it should eventually quite down. :) Good Luck! <3

Ok,first hold your cat's paws while wearing heavy-duty gloves and a good jacket(denim is best!)and bring the dog in.Then, just hold the cat Далее to the dog until they get used to each other.It worked with my cat, R.C.,who used to hate my dog.now they curl up together and sleep together.

give them their own personal spaces, and put the cat`s Еда dish by the dog`s.