Hi Beth,
I would not say that the problems you are having are "typical" of a CBR.
Normal grooming for a CBR is minimal. Normally, I only bathe with soap when a dog has gotten into something stinky or greasy or to speed the shedding process. Otherwise, an occasional rinse with the hose and a weekly brush with a coarse brush is all that is necessary. When shedding I will use a slicker brush to remove the undercoat...the furminator would do the same thing but I would only use it when they are shedding. Otherwise, the undercoat serves a purpose and should not be removed. I'm not sure how this changes when you mix with border collie?
If your vet doesn't have suggestions I would try things like Omega 3-6-9 supplements, changing to a food with no wheat or corn (most common food allergies), trying a fish based food, maybe even trying regular baths with a soothing shampoo (careful with this one - it could make things worse). You might also investigate seasonal allergies, worms, skin infection, etc?
Hope this helps.
Veronica