Basic respect for the client as a human being has not been met as supervised access means that she is allowed to see the child, albeit supervised.
There are some constraints in working in a special needs school such as the safety for the other children in the school. Thus, going to the FSC might be a better avenue for more family type work as the social workers in school would be more focused on the student. It is understandable that Mdm Yang is worried about her child as she is the mother and has the responsibility to take care of her. In addition, she also has parental rights (supervised) to see her child.
The social worker is in a dilemma of complying with the Principal (her boss - ie in a position of higher authority and power) and making the referral to an FSC. As a social worker, one should advocate for the client, as the client is not able to speak up for herself, given the circumstances. Perhaps, the social worker could look into how Mdm Yang could have some safe time with her child so that this will help to bring down some of her anxiety. Moreover, the child might have been pining for the mother as there might be some attachment issues at play here. I do not see any harm in updating her about the child's progress as it may also help to abate some of her anxieties. On the other hand, the FSC might be able to provide the client with the financial help the school is unable to provide. It would also be good to ask her what she really wants and how the social worker could help to ensure that her needs and wants could be met safely. Furthermore, the child could be asked similar questions.
Some information, such as the child's chronological and developmental age and the relationship between the social worker and the father, are not mentioned. Mdm Yang may feel isolated, rejected, helpless and hopeless and might want to join a support group where she can meet like-minded people or people who might be facing similar problems as her.
Also, the principal has to take into consideration the fact that the father has been given custody, although some supervised visitation rights have been awarded to Mdm Yang. The question would be whether the school is the best setting for Mdm Yang to have supervised access.
The social worker's attitudes, values and beliefs about foreigners, special needs and custody issues, and anxious people (i.e the quickest/easiest solution would be to pass the problem to someone else eg FSC worker) might be at play here. Clinical supervision would be beneficial for the social worker.