Honestly, it's fairly typical behavior of a 3 year old. I've had four kids so far. My first two weren't as bad as #3...and my 4th is only 14 months, so she hasn't gotten there yet. My #3 has had quite the temper. She can scream like no other kid I've ever heard!
I think it might help if you approach it that his behavior is actually quite typical for his age AND for his personality (because there are some super easy going kids that don't do this...but most do). Seeing a therapist for you guys as parents might help. It might help give you some parenting tools to react in a way that might help get better results.
Just for some ideas...my kids when they were three weren't ready to sleep in their own rooms. They go to sleep in there, but at night, they are allowed to come in our room. Right now only our 3 yr old is in our room, but we had a total of three of them in there for a while! They had little spots next to our bed. I used to be so scared when I was a little kid and always had to stay in my room no matter how I felt. I decided with my kids, they could keep coming in our room until they felt safe. So...I know that's not the most popular idea, but it is way less stressful for us as parents. When they get older, it's easier to have them stay in their room.
As for the temper tantrums, I'd look into his diet. Make sure he's not getting sugar, fast food, or things like that. It can REALLY affect a child's temper and their ability to manage it. If he's good with those things, then when he throws a tantrum, I would get on his level, see it from his point of view, and...try to give him a hug. It doesn't mean you undo anything you did that might have caused the tantrum. Such as, if you told him to not play with a certain something, and he threw a fit, you don't then tell him he can play with it...but you can comfort him for feeling upset about it. Even saying something like "Oh, I know that has to be soooo frustrating to want to play with that and not be able to. If I were little, I would probably feel upset too." With my kids, oftentimes this calms them right down. They might want to chat a little and express their feelings some, but then they are good and ready to go.
If the tantrum doesn't stop, I do put them in a positive time out. It's a place where they can go (their bed) and sit and look at books and relax. It's not meant as punishment. If I can, I will stay in there with them and help talk with them about things. But sometimes there is the screaming and no way that you can reason anything with them. If that is the case, sometimes they just need to be allowed to scream in a place that is respectful to other people - as in, not in the middle of the kitchen or living room;-) So, I'll take them into their room and let them scream.
By the way, I'm basing my answers here off of a book called "Positive Discipline" by Jane Nelsen. She has one for preschoolers. I really like it. It's given me a way different approach to parenting. I used to think if I hugged my kid while he was throwing a fit that I must somehow be telling him it's okay to throw a fit. But...that's not what happens. Instead, they calm down WAY faster and feel like their feelings matter and that I heard them.
I'd also see if hubby working from home might be part of the issue. It's hard to work and take care of kids at the same time. I imagine it must be a huge struggle for your hubby to make sure he's giving them all the attention they need during his working time. That could also be a huge reason for the crazy behavior. I know that when I get preoccupied with my own thing (even if I HAVE to do it), if the kids dont' get the attention they need, they behave WAY worse. I'm not sure what you could do about it. Is there anyway he can do his work while you are home? I'm not sure what type of job he has.
Anyway, hope that helps a tiny bit. Best of luck!