What to do when a Windows Update (KB4480970) breaks your computer?

Will my system try to reinstall KB4480970 tonight?

This entirely depends on your system configuration. Windows 7 allows you to select which updates will be installed. You will want to avoid installing KB4480960 and KB4480970 until a patch which resolves the known issues with those updates is released.

Do I just need to disable automatic updates?

You should configure your system and install patches manually until the issue is resolved.

If so then should I disable them until perpetuity?

You should absolutely not disable Windows Update in perpetuity.

how do I know when I can turn them back on?

Windows 7 SP1 and Windows Server 2008 R2 SP1 update history has every recent patch released for Windows 7, you should watch this website, until an update that specifically mentions this known issue is resolved.

Known issues in this update

Symptom - Local users who are part of the local “Administrators“ group may not be able to remotely access shares on Windows Server 2008 R2 and Windows 7 machines after installing the January 8th, 2019 security updates. This does not affect domain accounts in the local "Administrators" group.

Workaround - This issue is resolved in KB4487345.

KB4487345 is a stand-alone package which can be downloaded on the Microsoft Update Catalog website.

This answer only addresses the specific issue cause by the KB4480970 patch you mentioned.

Microsoft has released hotfix KB4487345 to resolve this issue created by KB4480970:

This update resolves the issue where local users who are part of the local “Administrators“ group may not be able to remotely access shares on Windows 7 SP1 and Windows Server 2008 R2 machines after installing the January 8th, 2019 security updates. This does not affect domain accounts in the local "Administrators" group.

The hotfix is not (currently) being distributed via Windows Update. Instead, you must download the patch directly from the Microsoft Update Catalog website.

You should install this hotfix on the computer hosting the network share(s) that users are not able to access.