Hi there let me see if I can help you.
I know what you are talking about the red yeast is the organism that grows on the damp fur and gives off an iron oxide which makes the fur red where it is kept damp.
This is particularly noticeable on white dogs.
So the usual solution is to look for the underlying problem causing the licking. As you have related dogs with the same issue I'd suspect allergies as a possible issue.
Paw licking and skin chewing is often a sign of allergies.
The skin itches from allergies, the dog licks and chews trying to soothe the itch, making the skin raw and allowing other infections to set in which may itch even more which makes the dog keep chewing or licking.
You can read about allergies and dermatitis in dogs here
Dogs can develop allergies to foods, and to inhaled items, and contact allergens such as rug cleaners, cedar beds, or chemicals including lawn chemicals or even flea bites.
You might want to try a different dog food that has no ingredients the same as what you feed now. Diets of Fish and Potato, venison, or rabbit etc. where the protein source is new and there is no grains in the food can work for many dogs for example.
You might want to see if some plain Benadryl helps with the itching. A common low dose is 1mg per pound of dog every 12 hours. If you choose to use that please read here about cautions
Or you may want to consult with your vet and consider doing allergy testing.
You may want to try a Chlorhexiderm shampoo from the pet supply store in case the problem is a bacterial skin infection.
This breed is also known to have low thyroid level issues and that can trigger skin allergies.
The vet can check for that with a blood test.
If your dog is not on a flea prevention that might also help. Just one flea bite can make an allergic dog itch all over.
Now there is also some potential that antibiotics will help with the red staining particularly around the eye area. This site goes over tear staining
and discusses within it the use of Tylosin which works for many dogs along with some other possible meds to use.
If you get nowhere working on this on your own I'd suggest seeing a veterinary dermatologist which you might find through this site
If these dogs are a part of your breeding program you may want to rethink that if your other dogs have no such problem. Introducing a health issue may not be the best choice if you have a good reputation for producing healthy poodles now.
Hope this helps you!