My Books Main Conflict!

One of the characters in my book named, June is struggling right now because her only family member which is her brother, Metias died.  Why I picked June instead of Day is because all problems that are happening right now are all pointing at Junes side.  Another conflict that is putting the situation farther is when the two characters meet then one of them walks away.  I don't think the charters will solve the conflict without causing harm because June was meeting up with Day so she could trap him a kill him.  As you can see she doesn't like him.  I think the the conflict is also Man V.S. Man.  Why I think this is because its pretty much character against character, they don't like each other, and want to kill each other pretty much.  But I think June wants to kill Day more than the other way around because of what he did to her brother and her only family member left.