First, why does he have to be dressed before breakfast? If there is no real reason for this, do breakfast first! I can see wanting him totally ready so that he can dawdle over breakfast until it is time to go, then he just gets up and goes. But still, that is an easy compromise if he is crying over food. Not that you should give in when he cries, but compromising on the schedule might make everyone happier. If you switch up the order a little and he doesn't START crying, you won't be giving in by letting him eat first. Some kids are criers when they first wake up. It takes them a few minutes to get their bearings when they get up. So let him eat and wake up the way you guys do with your coffee.
He DOES have a reason to cry in the mornings. This is a horrible way to wake up. He doesn't understand why your husband is being so mean, and why you are leaving him there with him. Especially if your husband is in a great mood the rest of the day. How confusing for a child! Your husband has got to stop yelling like this. Yelling just leads to more crying, it is a vicious circle.
I agree with the others that you can't give in to the crying. Infants show need by crying. Two year olds can control themselves. As long as they aren't scared and hungry and confused, that is. I would also try to calm my son's crying if Dad was screaming at him, your son is afraid. But the key here is to not let it get to that. If you side with your son, your husband is the bad guy. If you don't comfort your son, he is going to feel abandoned by you. My dad was a screamer. I know what that is like to grow up that way. But as far as tantrums and whining go, I wouldn't give in. With my son, when he gets whiny, I firmly tell him to use his happy face/happy voice. I have instructed him to smile while he is asking for whatever it is that he wants. He can't quite whine while he is smiling. If he is crying I make him take deep breaths until he stops. He cant cry while taking deep breaths. Then he has to use the happy face. I don't listen to him until he does. If its a full on tantrum, I leave the room and make him stop and behave before I will listen to him.
It's going to take some time before your son stops crying for you probably. I am sure he doesn't want to deal with Daddy in the mornings, and it is going to take some time, with your husband NOT yelling, before he will be easygoing about it. The first step is your husband's to take, he needs to control himself. And then you guys are going to have to give it time while your son learns to trust dad and control himself in the mornings. And you can't let your son get his way by regular crying. Does your husband apologize to your son when he yells? He needs to. But the behavior has to change too.