I've not read the whole thread op, as it seems mostly filled with people saying your kid is a nightmare and it's all your fault etc. People just like to stick the boot in.
One thing I would say, is giving in when you've said no, because he's upset - yeah, that's not great. I'd be stopping that. I know it's hard (been there) but you do need them to understand that you mean what you say.
For the other stuff, I do think dh is too harsh. Shouting at a little kid, not okay in my book.
I would really recommend the book "how to talk so little kids will listen, and listen so little kids will talk" (there's a general kids one too but the little kids one is probably more suitable for your sons age). It's eye opening and really helps you to understand how kids are responding and why, when we interact with them. Would be really useful for you and dh to read and think about how to get on the same page with this, as your opposite approaches on this won't be helping.
Honestly I had a hellish time with ds when he was just 4. Omg the tantrums! He would go from zero to kick off in a split second, wouldn't listen, would be violent and run off. Glad I didn't post on here, if the responses of "you're a shit parent and your kids is a spoiled brat" are an indicator of the advice that faces these issues. It was a phase. We weathered it with boundaries, consistency and compassion, and DS is now 5 and an absolute joy. He's intelligent, kind, empathetic and fun. He knows how to behave well and doesn't show any of those negative behaviours any more.
Try and sit down with dh and have a proper chat about how you want to parent your son and what boundaries you both think are important and try to get on the same page with things. Your son needs to know that you mean what you say, but he also needs to know that it's okay to have big feelings sometimes. And at 3, the only way they can often express these is by crying, shouting, throwing. He doesn't have to words yet to label these feelings and he needs you both to teach him (not for dh to be shouting him down so he is too scared to be upset and learn to bottle it up)