"I don't want to be too harsh with her as she was abused"
There's your problem. Any time we dwell on the past we decrease our effectivity in training. We have to 'work with what is in front of us', and nothing else.
Here, I use 'punishment' to mean any training method that DECREASES the likelihood of a behavior. I do NOT use the word 'punishment' with a picture in my mind of a beating or going nuts and yanking the snot out of the dog for a half hour or making it yelp and cry in terror. I use 'punishment' to mean a method that decreases a behavior. ANY method.
Because training dogs ALWAYS means using only the amount of punishment that is needed/effective and not one bit more, the dog's past doesn't really come into it. It's based on how the dog behaves - RIGHT NOW.
There are two problems in training - overdoing punishments, and UNDER doing them. There really is a 'sweet spot' in punishment, where the dog learns the behavior is not wanted, but the trainer is doing as little as necessary to get the point across. If the behavior lingers on and on, it just really is not an effective punishment. The behavior should stop very quickly if the punishment is effective. 'Punishment' is something that decreases a behavior. 'Effective punishment' stops a behavior in a few sessions.
There ARE dogs that cringe any time they are punished. Either after abuse or just because of their nature. There one has to use one's judgement and common sense. One needs to be effective and get the message across, and it would be nice if one could get a method that didn't cause cringeing.
If a dog is excited or startled beyond a certain level, he is LESS likely to connect the punishment with the behavior. BUT - cringeing is also a natural appeasement gesture in the pack. It doesn't always mean the dog is not learning or is hysterical. Look at the dog's overall behavior - is he learning that the behavior is unwanted? Or not? So be careful. There is a fine line between decreasing a behavior and overdoing a punishment.
You have to forget what happened in the past and just deal with what is going on now. Punish the behavior you don't like, reward the behavior you like. Do it quickly, because otherwise the dog will not connect the behavior with the punishment.
Often that means the dog must be on a leash to get the correction in time, or seconds will go by before you can punish him, and then it's too late. If the dog gets away with the behavior, remember, all HE sees is that sometimes the behavior is allowed and sometimes it's not. If the behavior is allowed off lead that's what he learns. He doesn't put a 'value' on it like we do. He just says, 'this is ok when I'm off lead, and not ok when I'm on lead'. Dogs are very pragmatic. They don't moralize. If you want him not to do something he needs to be punished every time for it, not just once in a while.
Guage your severity of punishment only by what works - start with a light, 'soft' correction and ONLY increase it if you absolutely have to. Try as hard as you can to make the point that this behavior is not allowed, but then become COMPLETELY calm and act very relaxed and casual. YOU have to show your dog that you aren't concerned and tense.
Remember that YOUR anxiety becomes the DOG'S anxiety. Be calm and confident. Don't tensely wait for 'the dog to do something'.
Punish the dog, then relax, and forget about it. Be calm, straightforward and clear. Watch for something you can reward, and reward it. You must stay calm and project a confident calmness, or all the punishment in the world won't work. Be sure you use only enough of a punishment to stop the behavior. You need to first of all protect the person he's reacting to, that's the most important priority.
You'll notice in a pack, that a pack leader does not ALLOW subordinate pack members to show aggression to each other. Almost any time two dogs start fighting, or even playing, the pack leader will step in and stop it. Keep in mind that this is a very, very ordinary and accustomed situation for a dog, and a dog can very easily learn to not show aggression if the pack leader says, 'no way'.
If you can, after the punishment, immediately give the dog something to do. Sometimes, all you NEED to do is just give the dog a job to do. Someone comes to the door, you say 'SIT', and give him a treat. That's all that's needed. With some dogs.
But say that doesn't work and you have to move up a step. So, for example, he growls and barks at a visitor. You have him on a leash, and immediately, you say, 'NO!', jerk the leash to give a collar correction and to get his focus on you, and say 'SIT!', and if you need to, guide him into a sit. The dog sits, and he gets praised. The visitor throws him a treat. And he starts to think, 'hm...this is a very interesting situation...'. Often you can very quickly get them to the point where they bark once at a visitor, and slam their butt down, wag their tail and look for the treat. It's really about timing and consistency.
Some dogs are born not quite the same, in very subtle ways that are - within 'normal'. They don't react to normal low key training. There are arguments as to why - I think that dogs just like people, can be born with less impulse control, less ability to suss out social cues, much more energy, much more aggression, and all sorts of other 'cognitive' problems. I think these dogs, just like a person with a learning disability, need more repetition, a more careful breaking down of the training into sensible steps, and things like that.
Too, I think some dogs are just born 'unstable'. They are always reacting as if they are cornered and being attacked. They can be dangerous. They kind of 'blow a fuse' at the slightest motion. If that is innate, it can be seen in very early temperament examinations, even at a few weeks, from simple neurological exams.
MANY dogs, however, acquire that sort of behavior due to bad training or abuse. But getting rid of it is NOT about ignoring bad behavior. Not wanting to discipline the dog because it was abused, will only cause it more anguish and confusion. It wants to be in a 'normal pack' with 'normal pack rules'.
I don't mean to imply that there is no normal range of reaction/behavior. There is. My Samoyed dog was a very, very tough dog, and required a very, very different correction than my collie. Even so - there were times when both dogs were excited and wound up and both needed a strong correction for them to even be distracted from their excitement, let alone stopped.
Aggression generally gets THE strongest corrections. A dog owner needs to think not in terms of what punishment he feels is 'acceptable training methods', he needs to think in terms of what works with this dog. If a quick jerk on the training collar stops this dog from growling and biting, that's what he needs! If nothing short of a rollover stops him, THAT'S what he needs!
One always has to be thinking that 'punishment' can be anything from a quiet 'no' to a very soft leash correction to something very extreme like rolling the dog over on its back or even something much more. Some people even use repeating an exercise as a mild punishment (I don't like to, as I may need to repeat an exercise just to refine it - I frankly never want a dog to think of a repetition as a punishment to be honest - there's just too much repetition in normal training!).
One thing I like to do with dogs that I think are 'over guarding' or 'over protecting', or just seem hysterical about a visitor, is to have that visitor throw him some food. NOT forcing the dog to go up and take it out of the visitor's hand. Let him stay back where he feels less threatened. You and the visitor chat and act relaxed and visitor can throw something irresistable at the dog - like Deli Sliced Smoked Turkey. One of the worst 'stranger aggression' problems I ever had didn't respond to the trainer's corrections. The dog needed to learn the visitor was not dangerous. Of course only corrections stopped a lot of the barking, but food has an amazing way of improving fear issues.
And the more scared the visitor is the more it tends to continue, so pick a very laid back visitor to practice this with.
Unless the dog is now in a new situation that did not exist before so the dog ALWAYS had this problem and it just didn't show, the behavior is acquired/learned, and can be un-learned.
There's a very distant possibility that aggression can be due to pain from a medical condition, or a developing tumor - so if it is getting to be a problem a veterinary appointment is not a bad idea.