Your perception of what a moral grey area is seems strange to me. So far as I have always thought of them, moral grey areas are situations in which there's a mix of goodness and badness in someone's actions/intent that is either closely balanced (such as mugging someone in order to feed your kid) or ambiguous in nature (such as pirating a movie to bring happiness and entertainment to your friends). Your first supposedly grey area in your thought experiment is in no way a grey area: the father was protecting himself and his family from someone with ill intent, and this good action heavily outweighs the badness of harming the guy or exposing his family to violence. In the second supposed grey area scenario the mother can only be said to have done something wrong if she knew she was purchasing stolen goods, the father's acts clearly lean toward being overall good, and nobody in their right mind would argue that Batman's negative actions in doling out vigilante justice outweigh the huge amount of good he does. Only the mugger's situation actually comes close to being a true moral grey area, but I'd wager that the vast majority of people would say that his actions were overall bad without needing to think too hard on it.

Grey areas are those which aren't easy to judge on first glance, not just anything that happens to have a mix of black and white parts. True moral grey areas are actions and situations which can only be judged by actually analyzing the situation and filtering it through your own personal moral code and values and giving differing weight to various actions based on what you feel is more or less good or bad (such as how murder is worse than theft, thus a murder would be weighted as being more negative than stealing something). People who say that they cannot make a judgment on a grey area are just lazy, they don't want to exert the mental effort it would take to go through this analytical process. Saying grey areas are bad because of this laziness is like saying calculus is bad because most people don't have the patience or knowledge to solve calculus problems that are randomly shoved in their face. This laziness extends to people not wanting to think about questions of morality in general, even when it's a pretty clear situation; the things mdk brought up are also true, and they contribute heavily to people making it seem as if the vast majority of the morality spectrum is shrouded in a grey fog that cannot be pierced. It's intellectual laziness, not a true problem with standard morality systems.

Speaking of which, your idea here isn't anything fancy or special. Everyone is well aware that grey areas (in the broad sense of everything not clearly black or white) are made up of both black and white parts, so emphasizing that point isn't any kind of breakthrough. Your "Pixelism" does the exact same things as any standard morality system (look at action/intent, weigh the good versus the bad based on your personal moral code, then make an overall judgement), you're just taking that optional deep analysis step and applying it to everything, even simple questions. Think of morality like liquid in a glass, good actions and intent are water and bad ones are oil, and the goal is to determine whether there is more water or oil in the glass. Let's say there's one of these hypothetical morality glass with oil and water in it sitting on a table and a person is told to figure out which one there's more of; someone operating under your system would immediately start siphoning off the oil into another glass so as to look at them side by side; someone with a normal morality system would take a look at the side of the glass to see if there's a readily apparent answer by eyeballing it, and they'd only start separating the stuff if there wasn't a blatant answer.

What I'm getting at here is that your way of looking at morality is impractical for most situations, and in the situations in which it becomes practical it operates in exactly the same way as any other normal morality system. Breaking things apart into black and white bits to analyze them all even for obvious situations just isn't practical, and I doubt you actually do so even though this is your system; when you look at a situation like a person harming someone else in clear self defense I'd wager your immediate reaction on the morality of it is that it was justified (or righteous, to use your word), not to tear the information apart to make a determination about it. When it comes to things that are true moral grey areas, anyone who's going to put the effort into analyzing and making a call on them is going to break up the good and bad things and weigh them against one another to make their decision, so your "Pixelism" thing isn't any different there.

It seems like you just dislike the idea of moral grey areas (due to a misunderstanding of what they truly are, from what I can see) so you've come up with these alternative terms to avoid using the term 'grey area' when talking of morality. In reality your morality thing is no different mechanically from the average morality system (just less efficient if you really do take the time to give in depth analysis to situations that don't warrant it), you just use some different words. Speaking of your special terms, I have to say your chosen name just doesn't fit. Talking about pixels makes sense insofar as you're talking about looking at the pieces that make up the whole, but the fact that they don't in any way fit with the "black and white only grey does not exist" thing because colors don't work that way makes it seem like a bad name choice; seriously, just look at all the grey pixels on the screen making your name choice look silly. A more appropriate name would be something more like analytical moral dualism, though that doesn't quite roll off the tongue. Another better choice of name would be to call it monochrome morality or something similar, since the term 'monochrome' is used to refer to things done in only black and white, which suits your idea quite nicely. Naming your concept after things that immediately contradict the core idea you're proposing just doesn't make any sense.