In writing a narrative on a personal conflict, I think you really need to identify your purpose in writing in order to consider what your attitude and tone are going to be. For example, your purpose might be to show that you were right and the other person was wrong. Or your purpose might be to show that there can be two different and legitimate points of view. Another purpose in writing such a narrative could be to show that you learned a valuable lesson from the experience. You can see that in each case, your attitude and tone are going to be different.
In the first example, your attitude is going to be one of wanting to persuade the reader of the righteousness of your position. If you seem to have an unreasonable and completely one-sided attitude, this is not going to be very effective. If you slant all the facts against the other person, this is going to be obvious and not very persuasive. It would be better to display a reasonable attitude toward the other person, so that you do not appear to be completely biased. Your tone should be reasonable, too, not ranting and raving, just presenting the facts.
In the second instance, you will want to strike an empathetic attitude, demonstrating that you have some insight into the other person's point of view. Again, your tone will be reasonable, showing that there are two sides to every story, that people can have legitimately different perspectives, and that conflict is simply one way that this surfaces for everyone.
For the third purpose, you should maintain an attitude of wisdom, a tone that suggests you have lived and learned. The conflict may have been resolved in a way that has taught you a valuable lesson. Or perhaps, looking back, even if the conflict was not resolved at the time, you are now finding that you have learned a valuable lesson from the experience.
So, you see, your attitude and tone are going to be a function of your purpose in writing. Every narrative should have a purpose, the point you want the reader to carry away after reading your narrative. And from that purpose, your attitude should flow!