Having the runs is quite normal, as they can pass the slimy afterbirths and the greeny discharge for a few days, although the oxytocin will help clear her out. The antibiotics will help clear up the infection. The goats milk can be given undiluted, its the nearest thing to bitches own milk. Try putting some porridge or weatabix in it if she will take it.
As for the bottle feeding, try to make sure the smaller more reluctant feeders (if there are any) get to the milk bar first, and bottle feed the good feeders. They can they go on the milk bar and get whats left. They are more likely to take to the bottle feeds, as they are greedy little so and so's!
Just lift the greedy ones out for a while and put them in a box with a blanket over a hot water bottle so the others can feed in peace.
Weigh the pups every day to make sure they are gaining weight, and keep a record, with a description of the pup so you know which is which.
Do try to bottle feed all of them at some point, as if she does have to go in to be spayed, she will be away from them for a time and if you have already got them taking from the bottle them it won't be so traumatic for them. She won't be able to feed them at first because she will be sore, and will also have the remains of the anaesthetic in her. You can hold them up for her to clean their botties though, as if she does not do this you will need to rub them gently with a warm damp flannel to stimulate them to go to the toilet after they have fed, as that is what the mother's tongue does.
Oh the joys of rearing a litter, these are the bits they don't tell you about!