One thing this OP says interests me greatly. that is that placement in the housekeeping job would be 'a lack of training.' If this is a private non-profit agency that is receiving state funding to train and place in private employment a certain group of hard to place individuals, there very well may be state and federal guidelines that must be followed. In this case, oh yes, placing a person in a job working for a member of the board would be frowned upon, would be a conflict of interest.
There are a great many of these contracting agencies out there, and federal and state auditors spend a great deal of time and energy keeping them from meeting their hiring commitments (We'll place these people at jobs that pay $15 an hour! We have a 100% placement rate!) by having the people come to their personal homes and wash windows for $15 an hour for one day. Or by using the funds to provide employment for their relatives. Or.... or..... or....
However, the OP is very mistaken if she thinks these board members cannot fire her if she crosses them. And she seems to have a great deal of genuine commitment to doing the ethical thing. A lot depends on whether this non-profit is operating solely on its own funds. If so, then I agree with the majority here, no laws are broken except that it has a faintly "off" smell.