In the position of a divorce and court appointed visitation for the missing parent, the child really has issues with the missing parent - this was part of the reason for the family breakup - at what point can this child refuse to see him without any court retribution to her mother ?

At age 18 the, no longer child, can refuse court ordered visitation. If there is major issues, depending how severe, you could go to court and try to get those visitation rights revoked.