Your kids should be able to access KA-Lite on your Raspberry Pi if you know its IP Address.
You can type this in the terminal
And should see something like this
In my case, my local IP is
Then, your kids can access it by typing on their browser
You can also use this link as another reference: https://learn.adafruit.com/adafruits-raspberry-pi-lesson-3-network-setup/finding-your-pis-ip-address