Hi there Delete768,
We understand you're asking how to delete or change your Mom's Apple ID email address. We're glad you've connected with us here in Apple SUpport Communities, and we can provide some guidance.
"When your Apple ID account is deleted, your account details and the data associated with your Apple ID are permanently deleted from Apple’s servers. You can't sign in to your account, and you won’t be able to access any data, content, or services that were associated with your Apple ID.
Photos, videos, documents, and other content that you stored in iCloud are permanently deleted; you can't receive any messages or calls sent to your account via iMessage, FaceTime, or iCloud Mail; and you can't sign in to or use services such as iCloud, the App Store, iTunes Store, Apple Books, Apple Pay, iMessage, FaceTime, and Find My iPhone. In addition, any Apple Store appointments and AppleCare support cases are canceled." Have a look at this support article for details:
How to delete your Apple ID account
Keeping that information in mind, you may want to simply change her primary Apple ID email address rather than deleting it entirely. Learn how here:
Change your Apple ID
We hope this provides some clarity about your options. Let us know if you have any more questions.
Take care!