If each person playing only plays on their own worlds, this is relatively easy to do as mentioned above. However, if everybody takes turns playing on the same world and builds their own stuff, in order to move only their stuff you will probably want to look into using structure blocks.
As I understand it, saved games are not user specific, so initially it sounds easy to just copy the saved games to the new laptop. But a game copied in this way would not update on one laptop to reflect changes that the other child made on the other laptop.
Wouldn't it be possible for one child to load a saved game and open it to LAN so that both children could play on the same world at once? Of course the updated game would only be saved on the host child's computer, and it would be a mess to keep having to copy the saved game onto the other laptop so that the second child could continue to play in the same updated world when the first child is not around.
If the saved game was on a network drive on a laptop that was never turned off, wouldn't both children always have access to the saved file? If they wanted to play together the one who opened the game first could open it to LAN.
I'm getting dizzy, I think I am over my head. Maybe the best solution would be to have only one child who plays Minecraft.
Anything in chests would remain in both copies of the world.
Things in personal inventories would be tied to the player/account, so if one kid is getting a new account and username they would presumably not have that stuff. So that should be placed in a chest before copying the world.
Is this the Bedrock (Win-10 edition) or Java version of Minecraft?
If it's Bedrock the file path given above is presumably not correct and you might be better off asking in the Bedrock section of the forum.
It was the talk of Achievements that made me think they might be on Bedrock, Java has Advancements, not that I can keep track of the difference myself, I look it up in the Wiki whenever I get confused.
I don't think it makes any difference when you copy the files.
After installing Minecraft or the launcher would have created the folder so you wouldn't have to, also you'd get an indication that that was the correct folder name, it's possible to change the settings so the game uses a different folder but you wouldn't be doing that by accident.
Minecraft wouldn't delete existing save files when you install it so, just whatever is easiest.
I wouldn't do it while Minecraft is running, but that's just out of principle as long as Minecraft isn't running that world (which it wouldn't if you hadn't copied it yet) it shouldn't affect anything.
just unpacking it and putting it in the /saves folder should work.
Have you checked that you haven't accidentally introduced an extra folder layer or something?
What you put in /saves should be a folder, with the name of the world (unless it was renamed), and in that a bunch of folders named "advancements","data","DIM1" etc and a couple of files like "level.dat".
That is the same /saves that contains the new world isn't it?
If you can't get it to work you could try uploading the backup somewhere and post the link so we could test it but it's unlikely to be corrupted.
And you seem to know the difference between Java and Bedrock so I doubt you'd be trying to load a Java save in the Win-10 version or vice versa.
Have you tried just copying the whole /saves folder from the other PC?
I know I messed up with the extra folder thing at least once, I tend to worry when uncompressing things that it might not have the files in a folder but spread them all over the place so I sometimes add a folder when compressing them.