I agree with the others - I would absolutely back up dad. I might say something along the lines of, "I understand Daddy has a big booming voice, but you need to listen to him and respect what he tells you. Your daddy loves you and is taking care of you when he tells you no. I think you owe Daddy an apology and a big hug."
If Dad sees that YOU back him up, he'll be able to take a more active role in resolving these conflicts and he'll have more patience in his voice rather than feeling defeated before he corrects DS. I bet he feels so stressed and frustrated right now and that is probably what causes the tone of his voice to be so angry/resentful/irritated.
It would also be a good idea for Dad to tell DS and DD that when he uses his big booming voice, that he's not angry at them even though he sounds that way. He just has a big booming voice, and some day DS will also have a big booming voice like his dad.
Personally, I was THE hypersensitive child in my family, and I jumped even at the sound of my dad's footsteps. My DD is the same way - just very sound-sensitive and emotionally sensitive, so knowing that, I play a lot with my own tone of voice. Most of the time, I am very calm with her, and use a cheerful animated voice (she's almost 2) when I make requests, such as "Stay where Mommy can see you!", which she will test but I'll say, "Oh? I guess you want to be all done?! Okay!" and then she'll stay within the boundaries I set for her (as long as I'm looking). But sometimes, I'll change it up and use my best big loud voice or a scary voice, almost growling at her, then I yell ARRRRRRRGGGGG!!!!! and chase her with my hands ready to tickle and we both end up giggling.
I do that because I want her to be confident and stand strong around authority figures, not feel shaky and panicked the way I always have.
So maybe you could suggest your hubby play games like that with the kids, using his big booming voice to chase them around like he's a tickle monster, and when DS does something he shouldn't, DH can shout "Oh! I'm going to get you THIS TIME!" And pounce on him, swing him up into his arms and say "You shouldn't have done that!! Now I have to tickle you for 3 WHOLE MINUTES!!! ARRRRRRGGGGGGGGGGGGG!!! HAHAHAHAHAHA!!!!" (just make sure he tickles him really lightly and doesn't restrain him, let him get away every 10 seconds and pounce again). Kids are always going to test the limits, that's their job. We parents need to keep firm consistent boundaries, but nowhere does it say we can't have a little fun doing it.
My DD tries to get into the trash, and keeps putting things in the toilet, and I just yell "ARRRRRRRGGGH!!! OH NO!!! ACK!!! AAAAAAAAAAAAAAAHHH!" in that same loud silly voice, snatch the object gently and put it in the sink. Then I reinforce in a very calm voice, "We don't put things in the potty. Yucky!" shaking my head slowly. If she tries again, I physically block her, then poke her tickle spots until she runs away. Luckily she's extremely ticklish.
This way she learns I am a formidable opponent to try to disobey, but she feels loved, gets corrected in a positive way, and then our focus is on our fun tickle fight, which usually ends with her being exhausted and throwing her arms around my neck for a big hug.