I don't want my brother to move back home during my spring break.
Why don't you want your brother there during your spring break?
I just want him out of my hair!
It's really disrespectful to your brother to want him not to be there. Accept your brother's presence, he belongs there just like you do.
So what will happen to my personal space?
Even if you don't have as much personal space, you should be happy you get to see your brother more. I'm sure he'll be happy to see you too.