Apple Event: May 7th at 7 am PT
Apps are forever tied to th Apple ID that was used to download them. In your case it's your mum's Apple ID.
If your mum has 2 factor authentication, a verification code will be send to her phone and must be used.
Now wind back.
If you are using your mum's iPhone.
First make it yours: What to do before you sell or give away your iPhone, iPad, or iPod touch - Apple Support
After that setup the iPhone using your own Apple ID.
If your mum want to share her books, apps and music purchases, she should setup see below:
Apps are forever tied to th Apple ID that was used to download them. In your case it's your mum's Apple ID.
If your mum has 2 factor authentication, a verification code will be send to her phone and must be used.
Now wind back.
If you are using your mum's iPhone.
First make it yours: What to do before you sell or give away your iPhone, iPad, or iPod touch - Apple Support
After that setup the iPhone using your own Apple ID.
If your mum want to share her books, apps and music purchases, she should setup see below:
Apps will always be tied to the account from which they were purchased and will always need to be updated using that account.
If the app on your Moms phone were purchased using your Moms account, then they will have to updated using that account.
As for authentication:
Why can’t I update my apps?
