“When a traumatized family moves in to a new house on a remote island and gets hauted by a bloodthirsty dead plague doctor—an overprotective mother —must find a way for her and her family to survive and force the plague doctor to cross over to the other side.

The fact that the mother is overprotective doesn't really add anything but length to the logline....Now, if she was an unbelieving mother then I could see some added conflict...good luck!

In addition to the above questions consider the following as well prior to redrafting the logline.

What is the inciting incident; is it moving to the house? Discovering the ghost? OR the ghost starting is haunting torment?

What family is traumatised? What does a traumatised family mean? What are they traumatised from?

Hope this helps.

is the Plague Doctor a ghost of sorts ? Is the family isolated on this island ?