Yes, just recently (at 12 weeks old!) I have had one of my 5 kids scouring with suspected cocci (actually it started after she ate green wet grass pinched from next door pen), I treat mine with Intradine (injectable) and have had good results, but you can expect a relapse about a week after the first bout. All quite normal, leave them in their mums/feed goatsmilk, but not milk replacer. I also put Rehydion into my milk bottles, it is really good stuff. Other than that free access to hay, but no concentrate/fresh greenery until fully cleaned up and then re-introduce gradually.
I have yet to meet a goatkeeper who didn't have cocci. My vet doesn't even bother to test for the cause of the runs at this stage, just treat immediately and it so far was always successful.
Re skinny mums - if they all had twins/triplets and are still feeding their kids I would expect them to be a bit on the skinny side. They will slowly get fuller again as the kids reduce their milk intake (btw my ewes look like coat racks too atm). Don't be tempted to increase their protein intake massively, it will just lead to diarrhoea. Branches, hay/grass, are best - and from what you are describing you are doing al the right things. My goats love thistles, docks and dried nettles, sticky willy (not sure of the botanical name), willowherb, brambles - you name they eat it.
Only thing I would do is get a worm count done, I would just take in one sample from one goat and treat all of them if they have worms.
I have had kids weaned by 14 weeks last year as I sold two and the person buying them didn't have any goatsmilk. They all did fine, but in my case I was able to reduce the milk gradually as they were on the bottle. Not sure about the strategy with kids on dams tbh, but would start by having the kids separated from mums during the night, then milk dams out in the morning and offer the kids concentrate and hay before letting them back out with their mums. Then increase time kids spend on their own? With lambs it is just a "cold-turkey" separation, not sure that woudl work with goats.
If they have got Rockies in their pens and don't use them, they just don't need them. You may find adding some goat mineral to their daily feed/concentrate ration helpful, I use caprivite. My BT's lick their yellow Rockies, the GG's don't touch them, but they all milk well...
Just stop worrying, kids are always one step away from some calamity (even my goatling nearly strangled herself the other day
), but most will survive and calm down by the time they have their first kids...