Do your goos have a dust bath available? If not, then getting some chinchilla dust and putting it in a container (tupperware tub works fine as its not going to be in the cage too long!) in the cage will see her "wash" herself really. Then you don't have to worry about getting her wet.
Sorry, I don't have that much degu experience, I'm more familiar with hamsters, but I wouldn't let Nancy and sister alone with the pups. I wouldn't separate mum from pups at all, even for a few minutes.
I think my priority would be keeping everyone safe - which you have already done by separating them off. Then, I would start thinking what to do with the other pregnant female and what happens when she gives birth. Then I would be thinking about what to do with all the pups, when to separate boys from girls. I think I would be looking for good cheap cages on ebay or elsewhere, because it sounds like you are going to need more space.
I don't think I would worry too much about getting the 4 current females back together, especially as you are going to have lots of babies who will give you lots of options to make happy groups who naturally get along with each other. It depends what your longer term plans are.
I wouldn't worry about the wee on her coat. She should clean it herself. The most I would do is wipe with a damp tissue if it was really bad.