Dinny,
I teach a lot of concealed handgun classes, along with other self-defense classes for both men and women. The best way I have found to convince women is this. Now you have to remain calm and take as much time as it takes, while not being pushy about it cause if you put them on the defensive, they will just block you out, and then convince them slowly and gently. I usually do this by establishing the end goal, and then leading them to the conclusion and how to achive it. "What is your ULTIMATE RESPONSIBILITY in life?" Most start with doing their job, or earning a paycheck, or taking care of the house while their husband is away, or something along those lines that, at least for the purposes of this conversation, is piddly crap. Eventually I lead them to taking care of their kids if they don't get there by themselves. I explain to them that the only thing they HAVE to do at the end of the day is go home to their loved ones, and protect their kids. Once they get that in their heads, they usually start turning around. Some have said that they would shoot to protect their kids but not themselves, so I remind them that the parents take care of the kids, so the parents need to be safe to be there for the kids, and need to be protected just as much. Also explain to her that SHE is not the criminal, she is the good person and good mother who is trying to protect her kids FROM the criminal. The criminal, as you have plenty of examples locally, has no values or morals, and is a lethal threat to you, her, and your kids. We just had a POS arrested here for raping a 2 yr old, I believe about 6 months ago, and we have women of all ages raped constantly all over our country. Since SHE is a woman, and if either of your kids is female too, some criminals basically see any female as entertainment, regardless of age, and they have no mercy. It is her job to protect her family when you are not there to do it.
Besides, like I said she is not looking for trouble, she is not the criminal. So she will not be killing the criminal that kicks down your door (should that happen, and I pray it never does). The criminal will have committed suicide, and chosen her as the tool of their death. The criminal chose to committ the crime that ended in their getting injured or killed, and she chose to keep her loved ones and herself safe.
IIRC, you have extensive medical training, so if you haven't yet, educate her on at least basic aid and anatomy. Once that is accomplished, explain to her that since she knows what to fix, she knows what to break also. Target effective areas on the assailants body. After all, she is not trying to kill him, she is trying to stop him from harming her and hers. However, she must not care in the least weather her stopping him results in his death, injury, or hopefully he gets smart and stops his aggression before she does send lead into him. And just as with your unit, if something happens to where she does have to act, make sure she has done nothing wrong, reward and praise her for keeping her and hers safe, even while the legal repercussions are going on. Don't ever make her feel like she did anything wrong in protecting herself and your kids, and try to keep her from making herself feel like it. Look past what she did to the turd, but rather at the positive she accomplished by doing it. You have seen the reactions and consequences in some of your guys in your unit, and possibly yourself. This is no different in how you deal with it. Do not disarm her because that will make her feel not trusted, and since the investigating LE agency will probably take whatever weapon she uses for the duration of the investigation, give her another to replace it. This is a psychological thing. If she turns it down, and she may, so be it, but it has to be her decision, not yours or anyone elses.
Just work slow, be encouraging, and teach her, at her pace. If you force her, she will get resistant and refuse to learn, so tailor the training sessions to her comfort, both lenght, intensity, etc. Just keep it fun if possible, and make sure she knows how to handle her chosen weapon and is comfortable with it. Eventually, it will become second nature and she will be able to use it as if it was a part of her, and will do so if you can get her to accept the psychological aspect of using lethal force if she needs to. Like has been said though, not everyone can so don't push too hard.
As to the dog, I was going to suggest that, but have an idea for a compromise. Is she scared of all dogs, or just big ones, or maybe just the type that she was attacked by? If it is a specific type, just get something else. If it is big ones, get something small. I mean, even a chihuahua can make enough noise to alert you and her when something is wrong and buy you time to get to your safe room, or your weapon. I have two dogs, and the small one is 90 lbs, while the big one stands as tall as I do when up on his hind legs. The big one is a year older and I trained him for defense and guard dog duty, and he does the job well. The smaller one is in training, and moving along well, but not quite where I want her yet. But even with this training, they are both very loving and friendly unless they need to act otherwise. Maybe you can get your wife around some dogs on occasion and let the dogs convince her that the vast majority of them truly are "man's best friend", and not like whatever the one that got her was like. And if you're ever down my way, y'all are more than welcome to go hit the range with me and go play, so just let me know.