Hi winston54
I have had occasional problems with SuperDrive and macOS since Catalina, possibly even earlier, where the OS seems to think the SuperDrive has a non-readable disk loaded and it gets stuck like this no matter how many times the Mac is restarted normally.
This occurs across several Macs that we use in our office so it seems a more generic thing rather than specific to one machine.
The usual solution is to boot the Mac into Safe-Mode just one time which seems to clear out whatever bit of information the Mac was holding on to and causing the SuperDrive to not be able to see a new disk inserted.
The other thought that occurred as I was writing this reply is that maybe your own Mac is licence coded for a different DVD region than the disks you are trying to read, and that might be the reason that it will not open the same disks that your daughters MacBook can read.
Try carrying out a Safe-Mode boot one time anyway to eliminate that possibility.
There is no need to do anything during a Safe-Mode boot, just start the Mac in Safe-Mode as described in the linked document below, after the mac boots to the normal desktop view leave the Mac alone for another ten minutes and then restart the Mac normally.
A Safe-Mode boot takes a long time and the Mac will behave very sluggishly while in Safe-Mode, mouse and keyboard will lag behind your inputs, this is normal.
Once rebooted in Normal-Mode after a restart everything will respond at normal speed again and perhaps the SuperDrive will be able to read your disks again.
How to use safe mode on your Mac – Apple Support (UK)
HTH
Will.