Hi, 

Unfortunately, no product will tackle the broadleaf weeds and not harm the Carex at the same time, since it is a sedge and not a grass. Hairy bittercress is going to die off soon as the weather warms so with all the other weeds, it wouldn't be one to focus on. You could try removing the flowerheads from going to seed to help reduce the spread and next year's population. Other than that, you would need to hand-pull or dig up the other weeds if you wanted to remove them. If you can tackle the largest areas, hopefully the Carex will start to outcompete the weeds and fill in the gaps so it can slow its spread. 

Another way to help would be to carefully paint or spray the weeds with a systemic herbicide. You could make a type of shield with a piece of cardboard with a hole cut in it to try to protect the carex. You would have to be careful, though, to prevent any harm to the carex that would delay them further from filling in.

Emily