Yeah, the things that can handle the cold just fine don't like too much water, if it floods. And if your seedlings were just small, they can get beaten down by wind and hard rain.
The trouble is, it will be getting late to start broccoli now (not sure about kale, I don't grow it, and the carrots will be fine restarted now). Broccoli doesn't produce well (sometimes not at all) once it gets hot and you are losing the window before it gets hot. You might have to break down and get store bought broccoli plants like you did with the cauliflower.
By the time it dries out, it will be time to plant beans and not too long after that (early- mid May for you I think) it will be time to plant squash and melons. You would probably be ok to start tomatoes again right now, if you are doing them. If you want peppers and don't have any started yet, you probably need to buy plants of those as well.