This can be done just using Copy-Item. No need to use Get-Childitem. I think you are just overthinking it.
Copy-Item -Path C:\MyFolder -Destination \\Server\MyFolder -recurse -Force
I just tested it and it worked for me.
edit: included suggestion from the comments
# Add wildcard to source folder to ensure consistent behavior
Copy-Item -Path $sourceFolder\* -Destination $targetFolder -Recurse