A chinchilla tail is just like your spine ( or sort of like your finger). It is made up of a bunch of little bones. It is part of the spine and is strong. That is why it is ok to hold the chinchilla by the base of the tail. Because it is a bunch of bones it is possible to break the tail. You can't snatch it. Just like your finger if you pull it, you can jam it, pop it, and sprain it, or break it. It is not mean to be shed like a lizard. Its not a good idea to grab the tail of a chinchilla that is running around the room. The tail is just a handle to holding an already still chinchilla.
If you need to catch one you can toss a towel over it to stop it and then grasp the tail.
My guess is that the chinchilla is eating the antibiotic ointment and that is what is changing the stool. I would suggest a trip to the vet to check on that tail. (also, now that the kits are 4 months old remember that Mom can not be around any sons and Dad can't be around any daughters. Inbreeding in chinchillas is not good)