You can do the following to start your application pool :
Invoke-Command -ComputerName "REMOTE_SERVER" -ScriptBlock { Start-WebAppPool -Name "MY_FANCY_APPPOOL" }
You can do the following to stop your application pool :
Invoke-Command -ComputerName "REMOTE_SERVER" -ScriptBlock { Stop-WebAppPool -Name "MY_FANCY_APPPOOL" }