Feel Bad, But I Find Myself Getting So Angry Ay My Nephew

Julian is three months older then Marlow. And I am getting so mad at him over meal time. I feel terrible, but I actually have to get up and walk away because my little 2 year old nephew can push me that far.
I am seriously getting to the point where I am going to tell my sister I can't do it anymore. That her son is going to put me in the loony bin.
And he is a really well behaved child usually. He plays quietly, he listens, he's really mellow. He goes down for a nap without any tears, he lays still while you change him. He is even getting really good at cleaning up since I started watching him.
Then comes lunch. And I could beat my head against a wall.
He will not eat a single thing that I put in front of him. Before he came along Marlow would get things like squash soup and crackers for lunch, and rice with peppers and steamed broccoli in it. And she would eat it, not problem. But I know not all kids eat like that, so I have modified the lunch schedule. Now we eat cheese sandwiches with pickles on the side, hotdogs and macaroni, tater tots and chicken fingers, cream of tomato or cream of mushroom soups, alphaghettis. That sort of stuff.
And she eats it, of course, my kids a garbage can. But Julian won't eat any of it.
It really bothers me how picky he is, and how utterly misbehaved he is at the table. He throws his food. On the floor, at the wall. And if he can reach it, he will snag Marlow's bowl and throw it too. So I sit very close to him. I try and take his bowl to feed him. I try to sneak in foods, I try to bribe him, to coax him. Nothing.
One day I let him sit there, with his food in front of him, for a full hour. And all he did was pout!
I watch him for free, and I waste stupid amounts of food on him. Every meal he throws on the floor is one I could of fed my own daughter. And it makes me upset that he is like this and his mother allows it. She doesn't care much. She acts upset that he does it, put then caves into his demands.
And what does he demand? A peanut butter sandwich. We are not eating that everyday, and I refuse to make two seperate meals to cater to him. I feel like a bully, but I can't constantly give in to his tempers.
Its getting so bad that I'm dreading lunch time. I have stopped mopping my floor twice a week like I used to, I just spot mop. Because he covers it in food everyday.
As soon as noon hits he basically camps out at the table, throwing a tantrum, until nap time, upon which he is escorted from the table straight to bed.
I really don't know what to do...it doesn't sound so bad when I type it out, but in reality it is unbearable.