$Username = "MyUser"
$Password = "MyPassword"
$RemoteComputer = 192.168.1.10
$credentials = new-object -typename System.Management.Automation.PSCredential -argumentlist $Username, $Password
$session = New-PSSession -ComputerName $RemoteComputer -Credential $credential

Invoke-Command -Session $Session {
    #You Need to re-auth to your remote drive now that you're in your session
    #Create a New credential object
    $PSDriveCreds = new-object -typename System.Management.Automation.PSCredential -argumentlist $Using:Username, $Using:Password

    #map a new PSDrive within your session using your new Creds
    New-PSDrive -Name "RemotePSDrive" -PSProvider "FileSystem" -Root "\\RemoteServer\Path\To\Share" -Credential $PSDriveCreds

    #Now you can copy from your PSDrive to the machine you're remoted to
    Copy-Item RemotePSDrive:\Myfile.ext C:\Local\Path
}