Hi JohnnyD277,
Welcome to the Apple Community.
You Mom's Apple ID password is likely in use:
eg: signed into Apple services like FaceTime and /or Messages, or to log-in to iCloud.
You may be able to locate it that way.
Else:
Apple Support have an article online to help with a forgotten Apple ID password:
Tip: First browse through all the methods available, and choose the one that suits best.
If you forgot your Apple ID password - Apple Support
If needed:
Also Note the section at the bottom of the above article:
"If you can't change or reset your password"
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Also:
you Mom might need to update her sign-in information with any Apple services that she is using.
What to do after you change your Apple ID or password - Apple Support
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Your Mom may want to use her new Apple ID password to turn off the forgotten recovery key.
"If you decide to stop using a recovery key, follow the steps listed, in the article below
on your iPhone, iPad, or iPod touch, and slide to turn off Recovery Key."
How to generate a recovery key - Apple Support
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All the best :-)