I think you will get responses to your question if you re-post it in a different legal area. This is not really an "ethics" question, and it does not appear to be a question involving a conflict of interest in the legal ethics sense. I suggest you try posting your question in an area like employment law or contract law. Also, you might want to consider consulting with either your company's in-house counsel or to a contract lawyer or employment lawyer in your area.
I say this because I believe the underlying legal issues here are something like the following: First, does the department where you attempted to send this worker have any duty or obligation to accept the worker, even if some other employee (meaning the ex-wife's mother) in that department has a personal issue with this new worker? The answer to that question might depend on the contract between your staffing company and the department or company that is getting workers from you (assuming these are two separate companies). There might also be issues related to internal policies of the company that turned the worker away, but I doubt that would affect your company's obligations (again, assuming these are two separate companies).
A second issue might be whether your staffing company has particular duties or legal obligations to ensure that an applicant who is qualified for a position gets the best position available and is not turned away for reasons unrelated to the applicant's qualifications. That could depend on both what's in the contract between your staffing company and the department or company you were referring this worker to, as well as any commitments or agreements you have with job applicants.
Whether it's these sorts of issues or something a bit different, I think you will get ideas and suggestions if you re-post this in one of the other areas I suggested.
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