Firstly I would get a worm count done on the adults, a coarse coat and skinny goat are two signs of worm infestation (do they have loose droppings too?).
I would also remove the kids now, especially if you are worried about condition of the nannies. Question is - do you want to continue to milk them or are they so thin (can you see their ribs and backbone comes up sharply) that it would be kinder to dry them up? However most nnannies are not fat at this time of year, so unless they are really skinny I would check their feed intake, give lots and lots of branches and a drench (like the Adam Henson one for goats, or a general multi-vitamin/mineral drench) would be good for them anyway. Then milk them out as much as you need regularly (once or twice a day)
My goats get a good sprinkling of linseeds onto their sugarbeet shreds a couple of times per week, also Capprivite, seaweed powder and garlic, and my coats are a lot better this year than previously. Omega 3 (or 6 - can't remember which one) is essential for smooth/shiny coats, and the best non-animal derived feed supplement for that is linseed.
I certainly wouldn't put them into this kid this autumn if you are oncerned about their condition.
Re worming the kids: Again worm count first, then treat as per recommendation from your vet. I have not wormed my kids yet, only nannies get routine wormer post-kidding, goatlings only if needed. They didn't this year. Also assess the likelihood of worms on your field - if not grazed by sheep for at least 12 months and goats came on worm-free you shouldn't really have a problem (only exception would be fluke).
The general advice for worming livestock is - only do it when needed and there is evidence of worm infestation. Goats are more sensitive to worms (being browsers they have not any built in tolerance, where adult sheep often can have quite a significant tolerance for worms), and need closer monitoring than sheep. Don't co-graze sheep and goats (horses and cattle are fine).Why did you worm your kids at 8 weeks?