I sympathise. I know what it's like to have a metamour you can't stand. And a bratty, disrespectful one at that. I also know what it's like to date a person like that. The difficulty is that the emotional (or otherwise) attachment can make it hard for the partner *in* the relationship to see it, or to let it go.
There are pros and cons to every personality trait. You sound like you strong-headed, feisty. That's great, because it means that you don't get dragged into unhealthy situations yourself. But, on the other hand, it may mean that you have a tendency to be overbearing and make your husband feel stuck between you and his girlfriend. It may even make him feel even less capable of sticking up for himself. In your husband's case, he's extremely forgiving, patient and understanding, I assume. On the downside, you might say he's a pushover.
I do understand your protective feelings. And, from your side of the story, she does sound like a nut job. But you don't have to date her. I really, really don't agree with veto power at all. There have been partners my girlfriend has had, who I haven't liked for whatever reason, but I've never actively said "it's time to get rid." I have, however, been on the other side of that recently, when a woman I was heavily involved with essentially had to break up with me for her own girlfriend, because her girlfriend was feeling too insecure. Sure, I absolutely understand it and empathise with her girlfriend - but it doesn't make it any better. I absolutely do not think you should call veto. It's not fair on your husband.
What you can do, as everyone else has suggested, is set up some guidelines relating to her personally. If she has to come to yours to even out the travel, like you were saying, then can you make yourself scarce often during those times, if you don't want to be around her? The rest of the time, I would advise doing as you have done and only offering your opinion when it is asked for.
The need for an apology is an interesting one. So often, we think of our marriages or primary relationships as this holy grail that demands respect from all secondary partners. For sure, I would have a major problem if I found out that any of my girlfriend's partners were trying to split us up. But if they just didn't like me? Why should they like me?
I actually don't think that 'Mary' was being disrespectful to you, or your marriage - she was, however, being vicious and trying to hurt your husband. I do not think that her apologising to you is necessary. My girlfriend is very similar to you in this sense - and I have been this way too. Her ex secondary really offended me once. When he realised it, he did absolutely nothing about it. I became stubborn and indignant about it, which put my GF in the position of having to defend him, which only pissed me off more... ~grins~ and right at this very moment, my girlfriend wants the blood of me ex, because they exchanged some vile words about our breakup. My GF was trying to be protective; just as you are. But all it has ended up achieving is more trouble. War between two women I care about. Don't put your husband in that position. Ask him to make his own mind up about her and not to come to you as often with problems.