I typically end up wrapping ADSI calls in a function, e.g. Get-ADSIObject – there are many others out there.
In this particular case, you are using PowerShell remoting with the default authentication, Kerberos. This means in your remote session, they trust that you are you, but they can't delegate that out to anything that requires AD access.
The simplest solution, assuming it fits your use case, would be to simply replace $env:computername with the account you want to query for.
You can run scripts to work with AD from any machine in the domain – assuming you have permissions to perform those actions. You don't have to remote onto a machine to do that. As Warren said with remoting you're attempting to delegate your Kerberos credentials and that isn't allowed by default remoting configuration