1) Don't worry - you didn't abuse him. Sometimes a tap/ light smack can be useful in punishment (I don't mean for not sitting on command but more of an attack on an animal or person type of thing). My dog often gets a tap on the nose for barking because he refuses to shut up - even trying to hold his mouth closed he still attempts to bark.
2) If they fight again keep your hands well out the way. I know its nasty to watch but they were probably just fighting over dominance (or playfighting). My dog can be nasty to about 80% of other dogs and will attack them if they sniff him. He usually gets a far as pinning the other dog down and snapping at it before "winning" and the other dog showing submission. For my dog that is enough and he will stop attacking. (obviously we try to put him on a lead before he meets other dogs to stop the fight before it happens)
3) He wont hate you forever. And once you've all calmed down and down some other things (watch some tv, have your meal or whatever) go and give your dog a cuddle. Give him some attention for doing something good (make him sit, lie, sit, lie and then give him a cuddle). He wont assosciate you with pain and anger. My other dog cowers when you tell her off and can continue to do so if you look at her sternly for 10 minutes after the telling off (all I do is "did you do this? What's this???" and after I ignore her for a while I come back and give her a cuddle and all is forgiven)
And I agree with the comments about your puppy trying to show dominance and become the alpha. YOU (and all humans, other pets, your older dog) all come before the puppy. Walk through doors first, eat first, greet humans and then after 5 minutes greet the dogs etc.