Remote access via Icloud to my mothers phone as guardian

If her iPhone was verified in the account , and you had created 2FA from Mac .

When www.icloud.com is opened from Mac , and click on continue with password it will prompt to enter admin password ( as it verifies the right administrator is signing in the account ) , as automatic login is off and two factor authentication is enabled , not necessarily the trusted devices iPhones are always synced with Mac that is with same Apple ID and password on the same network , however they are verified in the account .

in these scenarios Mac acts as trusted device , however if you want still to get codes on trusted devices don't sign in with admin password and click on cancel and can get codes on desired trusted device and then access account see Read Two-factor authentication for Apple ID - Apple Support

Get a verification code and sign in with two-factor authentication - Apple Support

Use two-factor authentication for Apple ID security on your Mac - Apple Support

The device can be anywhere but it needs to be added to the account as a trusted device. But, downloading a device backup isn’t really a solution as you would then need to erase a device and install the backup.

You can only authenticate on devices that are trusted on the account.

Is no an option on I do t have access to that number to enter another one??