Hey there George Hilton,
Thanks for reaching out to Apple Support Communities. I understand you’re having issues moving one of your Photos libraries to the trash bin on your Mac. I’ll be happy to help with this.
If you haven’t already, open the Photos library you want to keep in Photos and if you use iCloud Photos, designate it as the System Photo Library. Take a look at this article for help with this:
Designate a System Photo Library in Photos
Then try moving the photos library you want to the trash. Make sure both libraries are not selected when you do this. Take a look at the steps under “Delete original library to save space” for more info on this:
Move your Photos library to save space on your Mac
If you still have issues, boot your Mac into safe mode and try deleting the library from there:
How to use safe mode on your Mac
Take care.