If you have joint legal , you can sign things for the school and bring child to dr's or appointments when child is with you.
CPS "might" take the case. You are in the middle of a child custody trial and they may just say you did it to get the upper hand. Can you go to the school nurse and their psychologist and have them see child. They are mandated reporters and if they see anything even without solid proof, they MUST call.
Find another psychologist, interview them first, see if they are willing to treat daughter and see if you like them. Make appointments on your time. The psychologist also is a mandated reporter and if she feels daughter is being emotional hurt at mom's, they would have to call CPS.
Once the phone call is made, they will contact mother or is some cases go to childs school and interview child before child goes home for the day. They will interview and get documentation from her. They are not supposed to tell her where the phone call came from. If no one is willing to help you, maybe take a ride to CPS and give them your proof and see if they will open a case...take pic of daughter with no eyelashes/brows. Reports from school, dr's notes from the past.
Not sure where you are in the court system, but you maybe able to get temporary emergency hearing that child is in emotional distress and needs help, either treatment, program, counseling. You can say that this past week change of circumstances were that child is pulling out hair. Do you have a law guardian? Can you call them and tell them the latest?