I agree with most everyones comments.
1. Boundaries - That was the thing that stuck out most. You MUST set boundaries with your brother as you would do anyone else.
2. Your happiness - If you are truly not happy with the situation and cant see anything good coming from you helping your brother then you may have to let go and find other ways to help him. Do you HAVE to let him stay at your house. I am sure that if your brother HAD to leave, he would find a place to stay unless you honestly dont believe he could take care of himself. This may be what it all boils down to. Sadly it is an option. Since it doesnt appear that way- lets go back to #1....
His children with whatever excuses they have for terrible behavior must be controlled. You are going to have to be a "parent" as well. It is your house not your brothers and you need to have some defined rules and consequences and some achievable rewards for those kids. Every adult in that house needs to be an authority figure. You are going to have to keep those kids busy - on a schedule, with a routine that you make the kids follow everyday - in order to survive. Most dads aren't good at this but moms are and your mother instinct is going to have to kick in if you want to survive these 2 weeks!
From the moment they wake up to the time they go to bed, your brother needs to be sure to keep the kids on task. Check around to see if there is a day camp or some type of lessons to get the kids into, make sure you are equipped with art stuff, and kid friendly stuff besides TV and video games. This is all doable and I think you will be fine but if your brother cant handle them, you will have to.
Sit down and talk to your brother about how you are feeling and make a plan of action together to prepare for the kids.
I would also give your brother a strict timeline for when he needs to be out and stick to it because if you dont he will never take you seriously. And to me that becomes him taking advantage of you!