Is the OP saying that his niece didnt get the job because she is English and neglected to inform the interviewers that she is of Irish descent? I think this is the subtext. That may be the case depending on the nature of the job and the interviewers. It might be that they would prefer an Irish person over an English person for various reasons. If the OP believes this is the case then she should subtly include the informations on the application or in the next interview.
Is the OP asking whether she should have mentioned her connection to an Irish Minister? That depends on the job, the interviewers and so on. She is better placed to answer that herself. No matter how much we ( and possibly the OP and his niece) might dislike the idea it is quite possible that a connection to a politician might be an added incentive to hire her. Again if she feels it might make the difference then, depending on whether her principles outweigh any moral abhorrence she might have to doing so, she should have mentioned it in a very oblique way if that were possible.
Is the OP asking whether she should have mentioned her connection to an Irish Minister? That depends on the job, the interviewers and so on. She is better placed to answer that herself. No matter how much we ( and possibly the OP and his niece) might dislike the idea it is quite possible that a connection to a politician might be an added incentive to hire her. Again if she feels it might make the difference then, depending on whether her principles outweigh any moral abhorrence she might have to doing so, she should have mentioned it in a very oblique way if that were possible.