After reading your post, I don't think you compare to the OP's neighbor. You seem to be very aware of your what you are able to do and not do. How you interact with people even if its not the way you might want to . The fact that you know or feel that you are not socially aware means that you are more aware or at least you care about what you are doing than the OP's neighbor.
As another person with some of the same problems, I can tell you that it is usually not that easy. I can't speak for Kamik, but I can tell you that in my case, I study etiquette obsessively, and have become pretty adept at determining what the norm is via observation. (I've also become a really good judge of character because of how much time I spend observing people.) However, when it comes to putting my observations into practice, I almost invariably flub it up because I'm nervous and overly self-conscious. The comment that DH most often would pass along was that I annoyed people in those situations because I was trying too hard. Other people say that it makes them uncomfortable to socialize with me because I hold myself at a distance and I'm so watchful that they feel like I'm judging them.
The thing is, these days the "rules" for social interactions tend to be somewhat loose. It isn't 1880, when the rules were the rules and nothing ever varied. People like me need ironclad rules if we're going to manage to participate without annoying other people, because the subtlety of circumstances is largely lost on us.
My DS is a diagnosed Aspie, and DH is convinced that I have it, too, but to a lesser degree. Most importantly in my case, I grew up with a mentally-ill mother, and so I never saw adults socialize when I was a child. I also didn't socialize outside of school after my father died, because my mother was very unpredictable due to her illness. Anything I know about social rules I learned from books, and there is a bit of a gap in translation between how it works in theory and how it works in real life. There's also the issue of class: I grew up working-class but now I'm middle-class, and there are some social chasms to cross there, too. (I fall into them face-first with great regularity.)
The OP can help her own situation by setting very specific boundaries for her interaction with this family. Regardless of the reason she is having difficulty, being very direct about what she expects will help, because the neighbor will either learn to do as asked, or she'll be offended and go away.
I can not imagine what you are going through and how what seems like a simple task to me may not feel that way to you. I know a lot of us have issues you can't see, but they are issues none the less and we should all be more sensitive and patient to our neighbors, co-workers, family, etc. You never really know what someone's situation really is. 
