I've never used anything other than DE and I find it very effective on lice and red mites....which I think may be the ones you are seeing as they suck blood. I always dust the nest and surrounding area with DE before I set a broody as I once had a nest become infested with red mites and the broody had to abandon it before the eggs hatched.
I would give the chicks back to the broody and put them in a new clean area with a dust bath containing sand/soil and wood ash and DE where they can clean themselves up. There is great entertainment to be had from watching a broody hen showing her chicks how to dust bath! Then clean out and dust the area that you had them in with DE. I use a soft brush and dip it into the DE and then brush it into all the nooks and crannies as that is where the mites hide. A couple of days after I've dusted with DE I start to see little piles of dead mites which look a bit like cigarette ash.
That is my experience and I just wanted to give an alternative view to the previous poster who for some reason hasn't found DE effective. I'm sure Sevin dust will be more effective than DE but there are concerns about the widespread use of such chemicals and I believe it is no longer available to buy over the counter in some countries.... these products always make me think of DDT and it's widespread use before it was banned..
DE may take several days to work as it causes death by dehydration rather than chemical poisoning but it has certainly worked for me.... I think perhaps people who haven't had success with it have just sprinkled it about rather than dusting it into all the crevices.
It is advisable to wear a dust mask whilst you are using it.
Good luck whatever you decide to use.