L., this is a very common thing among fathers. I know many, many loving fathers who just can't take the crying. My husband was one of them (not nearly so much with baby #3).
I'm not saying that he's right, but he isn't alone in how he feels. Now, I can't condone the yelling shut up at a 4 week old, but men are programed differently than we are.
Now that that's said... You had a baby 4 weeks ago and sister, you are seriously hormonal. I've been there 3 times and I know. Everything is out of whack for you right now and having your dh yell and your baby isn't helping you.
Having a new baby is super stressful for both parents. But even more so for you. You're body has been through so much and it's going to take some time. I think you need to ask yourself, are you over sensitive right now? Is it normal for you to cry in this type of situation?
I'm not trying to place the blame on you but to help you see the situation clearly.
Addressing something like this shouldn't happen during one of her crying jags. It's already a tense situation and he obviously feels defensive. The best time to bring it up is in the light of day when everyone is sane.
You two need to get on the same page. Sit him down and tell him that you realize that the night time crying is h*** o* him. Ask him what you can do to make things smoother for him. I know this may sound like you're accepting the blame. You're not. What you're doing is opening the door to conversation instead of making him feel like he's being attacked. It took me several years to figure out this approach with my DH and it works.
Once you get the conversation going, calmly explain your concerns. He needs to know that you know that he loves his daughter but what's happening right now just isn't working. Yelling at her won't make her stop. Talk about ways to soothe her and calm her.
Talk about boundaries, as well. What you both feel is appropriate things to say to the baby. He can always do what my dad did. In the sweetest, nicest voice, sing my sister horrible things. I know it may sound horrible but think of the lyrics to rock a bye baby. Those lyrics were from one frustrated new parent. All my sister understood was the voice, not the words. She was happy, he got to let off some steam.
The thing is, the more you make him out to be the big bad monster, the more defenisive he'll get. I've been a first time Mom and know what it's like to hover. But , he has to learn as well. Asking him if he needs anything when the baby's crying or offering to take her if he's reached his limit is one thing. Getting in the middle when he's trying to deal with the situation isn't going to get you two anywhere. If he declines your help, as hard as it may be, you have to walk away. If he is as good with her during daylight hours as you say, you're daughter isn't going to grow up thinking he's a monster. OTOH, he needs to figure out when he's reached the end of his rope and to call in the cavalry (you).
He needs your support, not your critisism. But he needs to understand what the postpartum period is like. I'm not a crier. But the months after my baby's birth, I was very emotional. I would mist up at commercials (that's not me) It's important that you both understand where you're coming from.
If all else fails, let him know that in even though you want to be supportive of him, that you're a team, you will NOT tolerate him yelling at the baby. It's one thing to be frustrated, it's quite another to take it out on the baby. Offer to help him come up with ways to handle it, or let him work it out himself. But that is crossing the line and at that point you will step in.
Good luck. It will get better. These first few weeks are some the hardest and most insane. Once the baby starts to settle down more and sleep more at night, things won't be as bad.
Good luck with your new baby. I know that everything will be fine.