So what have you done to help your cat? Have you taken him to the vet for a complete checkup; including blood work and urinalysis/fecal? Have you tried separating him from the dog and doing a gradual reintroduction? Have you used pheromones to try to calm him? Have you tried Feliway diffusers? Do you pay as much attention to him as you do your dog? How old is he? Has he ever been wormed? What kind of dog do you have and how old is it? Has the cat ever had his shots?
Yes, it may help to have him fixed. It may take a while for the testosterone to abate but I have seen some remarkable changes to some of mine after being neutered. You will need to give your apartment a head to toe cleaning in order to get rid of all of the smells of him spraying. You can clean with a regular cleaner and then use a mix of 1/4 cup vinegar, 1/4 cup rubbing alcohol, 1 cup water and spray it very liberally in the spots where he has sprayed.
What he is doing is called redirected aggression. He, for some reason, does not like your dog. The dog is his target. If you take the target away during an altercation then the cat will redirect to you, your husband and your daughter. He needs to be completely separated in a small room to calm down. This is not his fault. Something has set him off.
What are the dynamics like in your home? Have you ever purposely let the cat and dog fight, maybe when the cat was a kitten, and thought it was cute and laughed?
There are so many many variables that could be in play here. Without knowing his whole history and seeing what goes on in your household it is difficult to know. What I would start with is a complete checkup and, of course, his neuter.
Here's a couple of sites to check out........
Hopefully they can be of some help to you.