The problem isn't specific to remoting: there are processes whose modules fundamentally[1] cannot be enumerated due to lack of permissions, even when running with elevation (as admin).
Since the errors report are non-terminating errors, you can simply ignore the (all) errors with -ErrorAction Ignore at the source:
Invoke-Command -Session $session -ScriptBlock { Get-Process -Module -ErrorAction Ignore }
If you want to capture the error messages, so you can determine the processes for which enumeration failed, use -ErrorVariable errs -ErrorAction SilentlyContinue, which silences the errors, but collects them in variable $errs for later inspection:
Invoke-Command -Session $session -ScriptBlock { Get-Process -Module } -ErrorVariable errs -ErrorAction SilentlyContinue
Specifically, $errs.TargetObject will list the process objects whose modules couldn't be enumerated.
If the intent is to find (and possibly kill) all processes that use a module (DLL) of interest, use the standard tasklist.exe utility or taskkill.exe utility with the /m parameter.
$moduleOfInterest = 'oleaut32.dll' # example DLL
$pids = (tasklist /m $moduleOfInterest /fo csv | ConvertFrom-Csv).PID
# Alternatively, use `taskkill` in lieu of `tasklist` above in
# order to kill the processes directly.
if ($pids) { Stop-Process -Id $pids -WhatIf }
Note: The -WhatIf common parameter in the command above previews the operation. Remove -WhatIf, once you're sure the operation will do what you want.
However, with this approach you may run into permission issues as well.
Note that tasklist.exe and taskkill.exe have a built-in remoting feature via parameter /S, allowing a single remote machine to be targeted.
However, using PowerShell's general-purpose remoting (via Invoke-Commands -ComputerName / -Session parameters) gives you more flexibility, notably the ability to target multiple computers in parallel.
[1] At least by default, elevation alone isn't enough; if anyone knows if there's a way to enumerate nonetheless, do let us know. This related question asks for that information specifically.