Crux: What are the boundaries of favors one should do for the child?
Potential consequences: On the positive side, one can ingratiate oneself with the child and her family. However, the CASA should not be buying gifts for them.
One possible solution: Offer to pick up a milkshake if the grandfather will reimburse for it.
Crux: How to verify your suspicion that the boyfriend is seeing Johnny in violation of established parameters.
Potential consequences: You could verify the violation. However, this would also violate CASA norms, and could antagonize the mother (not to mention the CASA supervisor).
One possible solution: This is probably unacceptable, but the CASA could drive to their home or building, park unobserved, and see if the two of them appear to enter. However, the CASA is not supposed to be a private detective. Alternately, do nothing, but certainly include the sighting in your report.
Crux: (Actually, the text doesn’t specify if the CASA has in fact picky-sworn with the mother not to reveal the secret.) One can see the arguments both in favor and against the mother gaining custody.
Potential consequences: The children return, the mother loses her job, and their financial situation becomes desperate. However, if the CASA reports the situation to the court, then (s)he loses the trust of the mother, especially if she has sworn not to tell.
One possible solution: It is the job of the CASA to report the situation, and all relevant information, such that the court can make an informed decision. Ideally, when asked to pinky-swear, the CASA would say, “Well, I can’t make any promises, but I’d like to hear your news.”