What is the problem and solution in My Brother Sam Is Dead?

The problem of the story is that Tim must choose which side of the war he's on. He's been avoiding taking sides for as long as possible, but as the war comes home to him and his family, he has to take a stand. Either he's a Patriot or a Loyalist.
And yet Tim's way of resolving this problem is rather novel. Instead of picking sides in the conflict, he resolves to be a pacifist. Disgusted at the behavior of both Loyalists and Patriots alike, he figures that the best course of action, indeed the only truly moral course of action, is to be hostile to the war. Among other things, this means that Tim gains a much broader perspective on things. Because of his anti-war stance, he's better able to see the fundamental humanity that unites both sides in this increasingly bitter, bloody conflict.