How do you prove this mother unfit?

don't deal with child protection services. their goal is to interject when abuse is happening. neglect won't fly because she is leaving child with family with the permission of said family. whether or not she is cheating plays no factor in neglect either. the child will have to be put in direct danger for child protection to be actively involved. contact your local prosecutors office and retrieve the phone number for your cities guardian en lightum. this is an individual who is appointed to ess custody issues and will give the court her take on the situation. her interest is with the child and she will interview all parties involved. contact a family law attorney as well. it takes a lot of time and money to take custody from a mother... but with persistence and proof that the child is better off with someone else it can be done. start a journal now of all times mom is away from baby. how much grandma cares for her and costs to do so. how long child her lived with grandma. your personal feelings about what's been going on. statements from other family and friends. good luck.