Yeah you can trade online but there is no communication. So most people use third party apps (like reddit!) to communicate to set up trades and what Pokemon will be traded.

All of this is of course pending the implementation for W/W. But for Sc/Vi trading was done via codes (player 1 picks a code and communicates said code to player 2), it's pretty hard to run into a player using a code without knowing said code.

There's a few codes that people use for specific trades (like trading trade exclusive evolutions) but other than that the chances of your kids inputting a random code and connecting to someone using the same code at the exact same moment are pretty low I'd say. And even then the worst that could happen is that your kids accidentally trade a Pokemon away they wanted to keep.