Answer:
Second option: Tell the editor-in-chief about her relationship to the pilot, and ask that the story be assigned to another reporter.
Explanation:
Second approach would be the most ethical approach a reporter should take in such a situation. The boss or (next in rank) should always be made aware of any issue. In such case, it is more likely that the editor-in-chief will assign the story to some other reporter. Even if he insist the reporter to carry on and be careful of any bias, the reporter can excuse on the basis of conflict of interest or any possible family conflict.
First approach would be totally unethical because avoiding any bias in such a situation is almost impossible. Even if she is 100% certain that there will be no bias, informing the boss is necessary so that no issue arises in future.
Third approach would be unethical, because the reporter's beliefs might be based. It is her professional duty to let an unbiased investigation be carried out.
Fourth approach is not ethical firstly because, the boss should be made aware and taken into confidence, secondly getting the article edited by someone else is less likely to remove all biases - after all it is an investigative article.
