Hi,
Based on my understanding , all the forests have a one way trust to the production forest . The production forest is the trusted forest ,right?
From what i knowing , cross forest Group Policy Management can be done successfully if you assign the permission successfully.
For your situation , if you trust is correctly, the users from the trusted forest can logon to the workstation in the trusting forest no matter the users are added to the administrators group in the trusting forest or not. But if you want the users to logon to the DCs in the trusting forest , you need to add the users to the administrator group or management it through the group policy :allow logon locally on the DCs.
For the Group policy management , if you want to assign the permissions ,logon to the GMPC server in the trusting forest with domain admins , and assign permissions in as following:
Delegate creation of Group Policy objects using GPMC
https://learn.microsoft.com/en-us/previous-versions/windows/it-pro/windows-server-2003/cc739363(v=ws.10)?redirectedfrom=MSDN#BKMK_Addgroup