It is much easier to be at peace with a disaster or war on the other side of the world ...
... than with the little troubles in one's own home or family. The people we are closest to, and most emotionally involved with, can certainly push our buttons sometimes ... even after years of Zen practice.
And that is just natural.
Some folks think that, if we are practicing Zen "right", we should be free of all fear, annoyance, worry, frustration. But I think that, if we were, we would lose so much of what it means to be human.
Sometimes the Buddhas in the old stories are portrayed as beyond all human emotion, but I feel that that may be a bit of fiction. As the stories were told, gradually the Buddha was turned into a golden statue or superhuman entity beyond human concern. Anyway, I feel that that is not the best way to be in our lives. One can be a Buddha with a heart!
I think that we should avoid to fall into excess harmful emotions, and try not to let them take us over. And I think that we should develop, as Buddhists, the ability always to know that all emotions are just our "self" playing games, like a dream and (in a very real way) they are not real.
I promise you that, if you follow this Zazen road for awhile, you will quickly realize that the way you experience all those emotions has become quite different from how you did before you took the Buddhist Way. The fear and other emotions will sometimes be there, but not like they were before.