Do all 4 of the cats attack the dog when/if they are alone? I was wondering if maybe one or two of the 4 were instigators and the other two got into the battle out of fear, adrenaline or whatever.
I have 6 cats and 3 dogs, have never had my cats go after any of the dogs. If the dogs get in their faces too much one might take a swing in order to save itself, but they never attack first. I have more trouble with the cats having random tiffs amongst themselves. But I do notice if 2 of the cats get into a spat, there is usually one or two more that will come tearing across the house to see whats going on. Sometimes they will jump into the chase and sometimes they take over in the fight and oust one of the originators.
Didn't know if maybe you could separate 3 of the cats for a day and see if the single one still attacks the dog. Switch off with all 4 cats, maybe you will find the one that is teaching the group to be mean.
Its a tough decision, we have had to rehome pets that just can't seem to fit into our family for one reason or another. Hope you find your dog a good home if you decide to rehome.