Is there a way to delete her PSN account from my PS3 account without losing anything?
There is a way to remove a user from a PS3 console, but you will lose the following:
Paid Content Downloaded from PlayStation Network
The account that bought the content can still download it from another console
Your console however, will be unable to use the content ...
I just looked at my box and there is no serial key on this game you should be fine to install it. There were several games with online codes in this era but this does not appear to be one. At most you might miss out on a promotional item that is no longer valid due to those having expiration dates on them.
It's the Manufacturing Code:
Printed on the discs or packaging of Sony DADC-manufactured CDs are
codes indicating master copies (matrix numbers) of discs. These codes
begin with a 4-letter prefix followed by a series of digits.
In your case:
BPDL - PlayStation 3 Blu-ray Disc Dual-layer titles
As I cannot find any other information, I'm guessing ...