I have been known to break down and cry on occasion, so you're not alone! You're under a huge amount of stress right now, between finances, your fiance's work situation, having 2 "new" kids, having been sick, etc. Just do what you can do, and don't work yourself into the ground trying to do everything for everyone.
You may need to sit down with your fiance when you are away from the kids (or when they're in bed) and let him know that you need his help with certain tasks. Be specific about what you want him to do. For instance, tell him that you need him to give the kids a bath when you're making dinner. Or tell him that while you are putting the kids to bed, he needs to wash the dinner dishes. I have learned that my husband has no clue what I want or need from him unless I am very specific. If I just say, "You need to help out more," it makes him defensive. But if I tell him, "While I'm cooking dinner, please help the kids clean up their rooms," then he will do it. You have seen that he will help when you are at a breaking point - I think he just may need some specific instruction before you get to that point.
It sounds like you're on the right track, getting some help with housework. Also something that has helped me tremendously as a working mom, is that I started going to Dream Dinners. It has actually saved me money on my grocery bill, which I did not expect, and most importantly it has made dinner prep go SO much faster. I am much less stressed out around dinner time now. I don't know if you enjoy cooking, but if it's not a task you love to do on weekdays, it's worth checking out Dream Dinners or another dinner prep place.
Hang in there, it sounds like things are going to get a whole lot better for you guys soon.