My kids (two boys 11 and 14 are the same way). As someone else suggested, this is likely just their personalities. I remember I fought with my younger brother like this growing up. My younger son is a very determined person and he wants his way all the time. His older brother also knows how to push his buttons to get him going and finds it amusing, so they spend half the day going at it. The other half of the day, they're absolute best friends. My solution for the summer is to enroll them in camps for the rest of the summer - they have two separate weeks of stay-away camps planned. I had originally thought they might be okay at home this summer between those camps and other family trips we have planned, since they're older (the oldest thinks he's too old for these day camps, but I found some that take kids going into 9th grade). I also think this past week is the worst as they're decompressing from the school year and getting used to not having a rigorous daily schedule everyday. But, like you, I too am going crazy and think the solution is to keep them busy. You might find that by enrolling your daughter in some day camps that she'll be much more tolerant during the times she does spend with her brother. If not, you'll at least have some peace in your day.