How to rejoin domain when trust relationship is lost

This happens because domain-joined computers automatically change their machine account passwords every 30 days. The client initiates its own password change and stores it in Active Directory. When you revert to a snapshot from a time before the last machine account password change, then the password stored in AD no longer matches the password that the computer is trying to use to log on to the domain.

To disable machine account password changes on the client computer:

1. Start Registry Editor.
2. Locate and then click the following registry subkey:

HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\Netlogon\Parameters

3. In the right pane, click the DisablePasswordChange entry.
4. On the Edit menu, click Modify.
5. In the Value data box, type a value of 1, and then click OK.

Also,

I don't think you can use the local administrator account with PowerShell remoting

Yes you can. You just can't use Kerberos. And since there's no mutual authentication without Kerberos, you need to add the remote computer to your list of Trusted Hosts in order to be able to use Powershell Remoting to get to it.