Can my non Jewish cleaning do laundry on chol hamoed? What if she does it without us asking, do I need to stop her if it is a problem?
No, she may not do the laundry on Chol Hamoed. She should be informed before the Chag not to do laundry for the duration of the Chag.
Shulchan Aruch O:C 543:1, 534:3. This will be prohibited either because as your employee her actions are being done as an agent for you, even if she wasn’t told to do this specific laundry. Or, even if she would be considered a “kablan” doing the job on her own terms when she wants, ther would still be a proble of maaris ayin, that it seems as if she was told to do the laundry on Chol Hamoed. Hence, she should be told to stop even if she is doing it on her own.