Powershell Get-Process cannot connect to remote computer
Well, I'm afraid you're giving away the answer yourself.
Your admin account on the local machine, does not have admin privileges on the remote machine.
Get-Process doesn't accept credentials, so when you run
Get-Process -ComputerName remoteMachine
you're authenticating as localMachine\Administrator, but when you invoke it and supply credentials, you're authenticating as remoteMachine\Administrator