Hi,
I'm not sure i understand you clearly.
If possible, you can share some screenshots here!
Feel free to let me know if there are any misunderstanding.
Here is my test lab:
Parent domain: fan.local user: f1 domain member: client
Child domain: cd.fan.local user: c1
When logon to client in parent domain and add C1 from the child domain into the local administrators on client, i can only search the C1 from the child domain:
Feel free to let me know if there are any misunderstanding.
Best Regards,