x2
With dusting the birds and sprinkling dust on their dusting area, I'd also clean out the current bedding, get rid of it, and sprinkle poultry dust on the bottom of the coop then apply bedding over that and sprinkle some poultry dust on top. I'd also in the process spray the coop nooks and crannies with either Permethrin spray or something like Orange Guard.
If they are red little mite like creatures, like specks of pepper that move slowly, it will be essential you attack that coop with a vegence as Red Roost Mites take hold in the coop itself and can be very hard to get rid of.
That is what I would do right now and repeat in 10 days, and again in 10 days if I see any evidence (and probably even if I don't).
If you are seeing bugs on the eggs, there is a definite problem of overgrowth.
If that doesn't work, come back to us and we'll walk you through plan B.
LofMc
Edited to Add: BTW...while there are the typical commonly found varieties, there are actually an alarming number of different external parasites that can invade a chicken. Rule of thumb is if it is fast moving, it is probably a louse (lice), if it is very small and slow moving, probably a mite. Mites tend to suck blood creating scabs (and itching) while lice live off of the skin, dander, and feathers and typically produce the most feather damage.
Further investigation at night with a flash light may help you figure out which one it may be, which can help with follow up treatment if the Poultry Dust and spray regiment above doesn't help eradicate (albeit you probably never eradicate to 100%).