You should probably read up on PSSessionConfiguration before you do this, so you understand the implications, starting with
help about_Session_Configurations
First, create a domain group called 'RODC PowerShell Users'. Put yourself in it, wait for replication, log off and on again. Check that you're in this group.
Second, from an elevated shell on the RODC, run this:
Set-PSSessionConfiguration microsoft.powershell -ShowSecurityDescriptorUI
(After the first, time you'll probably want to use -Force
but it's useful to see what it's doing.) Hit Y when asked to confirm.
After a few seconds it will display the Permissions UI for http://schemas.microsoft.com/powershell/microsoft.powershell
Click Add, enter your group name in the dialog that appears, and click OK.
In the "Permissions for RODC PowerShell Remoting Access" box, start with Read and Execute. (You may need Write or Full Control, depending on what you want to do.) Click OK.
Then enter Y in the PowerShell window to confirm you want to restart WinRM.
From your remote box, assuming you've already set up remoting on the RODC, you should now be able to run:
Invoke-Command -ComputerName server1 { $env:computername }