^^This is the right way to see it.
Just curious about this phrasing. Most people have 2 parents. And most peoples’ deceased parents would not live anywhere. So why would you say your “surviving parents” instead of just your “parents”?
this is so much better than all the other answers; Miss Manners rocks!
And for all the people thinking the OP should “just” have let them in so the kids can go to the bathroom: kids (or anybody) needing to pee or have lunch or whatever is even more reason not to just drop in on someone expecting to take care of it at their house.
I think the OP was absolutely right to not let them in, while doing it in the Miss Manners style would be ideal, at least she set a good example for those kids - on not being a doormat, I mean.
Mind you, I actually think it’s kind of sweet when somebody who just happens to be in the neighborhood swings by on the off-chance that they can visit with you, although even I would definitely prefer a heads-up text message in advance rather than complete and total surprise.
But as thorny_locust noted, the only thing that makes “dropping in” attempts even marginally tolerable is complete readiness to take no for an answer. Once you start trying to argue with the “droppee” about whether or not they’re available, yeah, you are firmly on Miss Manners’ Naughty List.
(Not to mention that I personally would be reluctant to let visiting kids into a seriously chaos-ified house on potential-liability grounds alone, irrespective of the etiquette issues. Furniture all over the place and piles of stuff taken out of now-empty bookcases and glass-covered wall artworks sitting around on the floor? I’m not a lawsuit-happy or lawsuit-paranoid person as a rule, but ISTM that it would take only a minor amount of heedlessness on the part of even a quite well-behaved child to result in some kind of fairly unpleasant accident. Don’t bring your unprepared small kids into an active work zone, even a domestic one.)
Words to live by. Or to abide by so that your kids may live. 
Exactly. When I go into that kind of cleaning frenzy (or did before I started having regular housecleaners), I keep going till I’m done, because when I finally sit down, I’m DONE. If someone dropped in when I was in the midst of that, I’d probably be as unwelcoming as the OP: “Hi, nice to see you, but I’m too busy right now for company. Talk to you later!”
Not necessarily. You’re not a mindreader. People are trying to create the correct impression that, in the old phrase, they’re not “at home” to visitors. That didn’t mean, and doesn’t mean, that they weren’t physically home – it meant that they weren’t receiving visitors. Your insistance that it must be deceptive to not answer the door puzzles me. I don’t see anything deceptive about it. You’re not telling the people at the door that you’re not home; you’re just telling them that you’re not answering the door.
Peeking in the mail slot was massively rude. I wouldn’t want to let anybody in who would do that. (At least, unless they had reason to think that I might be passed out on the floor; which seems to me the only excuse for that sort of thing. And I mean that you do need to have reason, not just that you assume that not answering the door means in itself that something’s wrong.)
I had a cousin who was a city person come to visit once. He said, Aren’t you scared out here with nobody around? I said, What’s there to be scared of? There’s nobody around.
(I do have good neighbors within yelling distance. I bet he didn’t, he lived in Manhattan.)
Misanthrope and introvert are not the same thing. Conflating the two sounds rather nasty to me; like telling people with limited physical strength that they’re just lazy.
And the OP may not be either one. The OP was working, and needed to finish the job. It wasn’t a paid job, but that doesn’t make it not work. Do you feel entitled to drop by anybody’s office or manufacturing plant and complain if they won’t stop work in order to entertain you? If not, then why do you think that people who are trying to get something done at home must stop in order to entertain you? (And if so, don’t you get shown the door a lot?)
This, too.
This is the way.
Now they have to be the “rude” ones for leaving quickly 
HOW DO YOU LIKE THAT YOU FILTHY DOORBELL RINGER?
That was mostly a flippant comment, but a lot of horror movies are set in remote areas which makes it seem more psychologically scary to me. It’s infiltrated my subconscious.
I’m with thorny locust on this. There are tons of reasons to not answer the door. I don’t answer my phone if I’m sitting on the toilet or watching a movie, either. In neither case an i lying. I’m just not making myself available.
I was not conflating the two. Nor was I saying any one poster- including the Op- was either.
What I’d have done is welcome them in, but explained I was in the middle of cleaning and could not stop if I was going to finish it. Then gone on doing whatever I was doing before they knocked. They would either offer to help or get the picture and leave (after using the bathroom). And if they did help, fine. I cannot imagine they would just stay and watch you working.
Incredibly rude on her part. How did you handle it?
Home invasions can happen anywhere. Around here if you have anything worth keeping you have a gate.
The bigger the better. Locking electronically, even better. Of course the gate can’t look too fancy. Or they’ll get the idea you have good stuff. If you have a decent house they might think you have money. (They’d be hard-pressed to find $18.74 here, in cash. Unless they found the grandsons piggy bank, he says he has $33.00.)
But we have stuff. Jewelry, guns, electronics. The lives of my daughters and grandkids. Only one man is here at night usually. And he couldn’t fight a home invasion group alone.
You dang right I would use a gun to protect our lives.
I’d give them what we had. That’s just stuff.
News reports say these types of crimes generally end in some people dying. Usually the residents.
These kinds of out of the way robberies are rampant. Alot are perpetrated on camps and lake houses.
You can’t leave anything unattended too long or you won’t have it anymore.
Father and step-mother (who I lived with for many years as a kid) alive, mother deceased. That’s three 
.
For that matter I technically have a step-father on the other side of the country. But other than some exchanged e-mails when my mother died I haven’t seen or spoken to him in ~35 years (nor had my mother, they were estranged). Also I never lived with him, so never considered him a parent. My step-mother more or less qualifies though - I’ve known her since I was in third grade.
People who when told ‘this isn’t a good time’ argue about it? I can imagine them not only standing there watching you working, but actively interfering, getting in your way and saying ‘you need to feed my kids, they’re hungry’ – and/or the children moving things around and quite possibly breaking some of them.
Thx. Didn’t think of that.
That’s why Mark Zuckerberg invented poking.
And throwing the stuff on the sofa and chairs on the floor so they can sit down, and whining if they get dirt on their clothing, while “Lark” chatters on endlessly about crap you have zero interest in, ignoring her kids having a ball throwing stuff at each other.
Pretty sure that people have been poking as long as there were people.