I 100% agree that the kids need to ask you personally. Give them a lecture on pool rules every single time as well then ask all of them for their $20 admission fee.
Well, I think the only four people at a time is going to cut way back on the other problems. I’m also definitely going to start making them bring a parent to talk to me before they can get in the pool (every time they get in the pool). This will do several things: One, I can remind the parents that the kid will have to follow the rules, or will be asked to leave. Two, I think a lot of the kids who come don’t plan on coming over to swim, they’re just wandering aimlessly around the neighborhood, and decide it would be fun to get in the pool. If they need to get a parent to talk to me first, it will certainly cut down on that. Three, it seems like half the kids that come are friends of a friend. Having to get parental permission will certainly cut down on that. Four, a lot of parents won’t want to be bothered coming to talk to me, so that kid won’t be able to get in the pool.
Right now, mudgirl isn’t home. But I’ve told her that any time any kid wants to get in the pool, they have to get permission straight from me, or her Uncle Bill (who lives with us and helps take care of her while I work). That way, it’s not mudgirl saying “You can’t get in the pool without your mom coming to talk to my mom”, it’s me laying down the law. So yes, I can be in charge. And also, she doesn’t come off as “the bad guy”, I do. But the less desirable kids in the neighborhood already know I’m a bitch. 
Well, make sure Uncle Bill is going to be firm on the rules when he’s in charge, then.
From the sounds of it, this is not an in-ground pool nor a large above ground pool. I’d guess that it is a pool that gets refilled daily, no filter or anything. I’m also not a lawyer, but these may not be covered by attractive nuisance codes.
It doesn’t get refilled daily, rather weekly. But no, it’s not large or in-ground. It’s not big enough to be covered by the attractive nuisance laws (we’ve checked).
Choppers, Nipsy
Nipsy, Choppers
:wonders how that helped:
Well, I encountered a whole new situation today, and I have to decide, overnight, how to handle it in the future.
A couple of kids who did not get permission from their parents to swim, just sat in our yard and watched the other kids, and goofed off, and were being obnoxious. One of them actually brought freeze pops over and ate them in front of the other kids. I went out and told him “It’s very rude to bring snack food into someone else’s property and sit there and eat them” and he stared at me like I was some sort of space alien or something. I also told them “This is private property, so I can make you go home any time you get on my nerves too much” and they tried to defend this by saying “But we’re not causing no trouble!!”
I thought about telling them that a double negative makes a positive, but their brains would have exploded!
So now I have to decide how I’ll handle kids who come to just “hang out” instead of get in the pool. By which I mean kids who are not ordinarily friends of mudgirl, which would be a different situation.
It makes me sad and frustrated that your little girl can’t just play in her pool and enjoy herself … 
A toaster and an extension cord sound like the perfect solution to your problem.
How about “If you bring food you have to bring enough for everybody”? and “My house, my rules, if you can’t behave you don’t get to stay.”
As far as I’m concerned, adults don’t have to explain to children. If you don’t like the way they act, send them home. Not theirs to question. Acceptable in your yard is defined by you, period. If their parents object, they can keep them home and watch the little heathens themselves.
Foreseeable trespassing children, in general, are liability factories for property owners. http://www.romingerlegal.com/Ohio_case_law/2001/2001-ohio-128.html (noting that only three states that “had not not either created a special duty
for trespassing children or done away with distinctions of duty based upon a
person’s status as an invitee, licensee, or trespasser,” and then recognizing the attractive nuisance doctrine.)
And see, *e.g., * http://vlex.com/vid/20402026
Try a large slingshot. Nothing quite as effective as launching a heathen over a couple of roofs with a slingshot.
But if even that does not work, just crate them up and mail them overseas.