I haven't read the replies, so forgive me if I'm repeating anything!
I noticed that your kids are three years apart, and your son is three. I'm not sure why everyone talks about the terrible twos, because I found three to be SUCH a difficult age: they are so emotionally needy and figuring so many things out, and trying on so many different personalities and testing their limits (which IME, includes seeing if you respond the same way every time). Adding a newish sibling to the mix can be tricky too. In retrospect, I can see there was a lot of jealousy with my DD...she'd had us to herself for three years, and now there was a baby needing (especially) me ALL THE TIME. And we had a lot going on, and not enough sleep...so I feel for you.
I can't address your health issues, but I think a lot of what you're describing sounds pretty age appropriate. I think regular, ample sleep (for everyone), regular meals/snacks, and predicatable routines (including logical, always followed through consequences) can make a world of difference. I know it's not a popular sentiment here on MDC, and I would love to be a mom that never yells, that is always happy, and has a kid who is predictably good all the time b/c I feed him/her perfect meals, don't let them watch tv, etc, but it is EXHAUSTING to try and live up to this ideal. We do the best we can, as much as we can. Kids don't always live according to theories, and I've found that the more I parent, the more I have to check myself. Labelling myself as GD, or AP can make me feel really boxed in and frustrated, because I compare myself to a book or an ideal. No one needs a mom that feels crappy about themselves.
Can you call in some help? Get some time for you? Even if it's just a bit of time to yourself once a week, it can make a big difference. You and DH need to sit down and make a game plan. We fell into the empty threats/bribes hole around that age too, and it only makes it worse in the long run. Come up with a list of natural consequences for actions, and talk it over with your son, and make sure you BOTH follow the same plan...consistency is key. Find some strategies for you and your DH to get more sleep (alternate sleep ins on the weekend, force yourself to go to bed early a couple of night a week, take turns attending to kids at night). You are totally in the trenches right now, in terms of meeting everyone's needs and it is so easy to put your own needs last...but you have to take care of yourself, or you get too tired to parent the way you want to parent. I totally relate to the feelings you're having.
IMO, kids thrive on rhythm and routine. This does not mean a set-in-stone, follow the clock schedule, but creating natural points on the day that are structured for loud, quiet, restful or playful activities. Right now is a natural time to build some routines that work for you and your family.
Good luck, and I hope you find a good starting point!