Each of the Turtles have shown different sides to their personality when it comes to being mad at each other. Yes Don would be the worse one to get mad at you, because it will take a long time before he's willing to sort things out. Though once he does forgive you, than you are forgiven. It's just getting to that point with him will not be easy.
With the other Turtles mad, well Raph is always angry any how. So they're all use to Raph being pizza'ed at them. Sometimes Raph pushes too far in his anger, and almost hurts his family or just take off to blow the steam. Though when that happen, the one Raph punishes the most is himself. Mad at himself for being so out of control. He's loves his family so much that the one who pisses him off the most, is himself. So he has an easier time to forgive his brother.
Leonardo does get angry, but at the same time knows where to go to let it out. So when he's mad, he trains to let his stress out, and also takes time to talk to Master Splinter. Being the one always left in control, has taught Leo how to help control his temper. After he works the steam off, he'd talk to who ever pizza'ed him off. Which is usually Raph. Though in the 4Kids series they give Leo a bit of a Raph type attitude, with running off when he's angry and taking matters into his own hands. And season 4 is whole other story.
Michelangelo is a hard Turtle to pizza off, but not hard to offend. Though he's very fast to forgive. He's gotten the short end of the stick all of his life. He's also a prankster and does things to upset his brothers. So he realizes a lot of it, is stuff he did bring down upon himself when his brothers do pizza him off. Mike will go out for walks, or play video games to work the stress off. Though will bounce back to his self in no time to say all is cool. One of the best samples of this is
The unconvincing Turtle Titan. He was hurt by how his brothers treated him, went out and did stuff. But when he came back, he didn't rub it in their face though it was on the news than he even denied it being him at first, and went to Splinter to train.
Now, ways they'd react to having a brother mad at them.
I know that Leo, Mike and Don have all had Raph mad at them in the past. They won't take horrible offense to it, and will realize he needs to chill out before things can be fixed.
If Mike's mad, sadly his brothers don't always take it serious cause they know that Mike will forgive them soon. They don't always realize just how much they hurt him at times.
When Leo's mad, it depends on the brother.
- Raph walks away. He's not going to put up with Leo like that. He gets annoyed with Leo as it is.
- Don would try to make amends with his brother, to make sure Leo is ok. If that doesn't work, he'll wait for Leo to come to him.
- Mike will make some sort of "I'm sorry" type gift be it food or something to try and cheer Leo up. He'd smile a lot to Leo to let him know things will be ok.
If Don is mad, his brothers would stay out of his way. They'd want to know how to help but first they'd have to find out he's upset. Don is the type that wouldn't really show it, he may snap a bit more, and be a lot more quiet. Though he won't come out and say he's mad, till he's ready to talk about it. He could be pizza'ed at his brothers for months and they won't know or they'd have a small idea... till he wants them to know.