OP:
Try this:
First, be powered down, all the way off.
Now, boot to INTERNET recovery (this is NOT THE SAME as "the recovery partition"):
Command-OPTION-R
at boot.
The internet utilities take a while to load, be patient "as the globe turns".
If you connect via wifi, you'll need your wifi password.
When you get to the utilities, open disk utility.
VERY IMPORTANT STEP:
Go to the "view" menu and choose "show all devices"
DO NOT skip this step!
Now, look at "the list on the left".
The topmost item is the SSD inside the Mini.
Click on it and then click "erase".
Erase the ENTIRE drive to APFS, GUID partition format.
Close disk utility and open the OS installer.
Start clicking through.
The Mini will restart several times, and the display will go dark for a minute or more, with no indication of activity. BE PATIENT.
When done, you should see the initial setup screen (choose your language).
At this point, either quit setup assistant (don't know if it gives you the option to manually quit), OR -- pull the plug out of the wall (really).
Now, it's ready to hand over to the grandkids and when the power on button is pressed for the first time, they'll see the initial startup screen again, and can proceed with the new setup.
If you PRINT OUT these instructions and follow exactly as I've presented them, I predict a 98% chance or better of success.
Good luck.