Skin Condition in my Golden

Question
I have a three-year old Golden Retreiver with some sort of skin condition, and I also have a four-year old cat, found her as a stray at about 2 weeks old.  It all started about a year and a half ago.  She started scratching uncontrolably, red skin, I bathed her, brushed her, my house is practically spotless, brought her to the vet, and the vet said that she had a her folicules closed so fast that it caused an infection (something like that), gave me a course of reasonable medicine for 10 days, and she was fine.  She also said she had an ear infection, gave me drops for that, it went away in a few days.  
  About two/three months later, it started again.  Brought her back to the vet and the vet told me that I wash her too often (about once every week or two).  The vet told me that she has two dogs and she has not given them a bath in over a year and she has tumble weeds in her house....that was the end of that vet.  But again, gave me a course of reasonable medicine, and it went away within a few days.
  She starting getting bad dandruff, brough her to another vet about five months later, red spots, scratching, shedding so much, vet said that she might have an allergy.  Gave me Cephalixen 500 milligrams per pill three times a day for 14 days (1,500 milligrams per day!) and Predisone for 21 days.  Within a few days, she got better, although I finished out the medicine.  He also gave me shampoo to wash her once a week with, which I did.  Brought her back into the vet two weeks later for a checkup, he said that she still had a little redness on her chest, and gave me Cephalixen 400 milligrams per pill three times a day for another two weeks. .
  Brought her back to the vet three months later, all started up again.  He did a thryoid test, that was normal.  Gave me the  Cephalixen 500 milligrams per pill three times a day for 14 days (1,500 milligrams per day!) and Predisone for 21 days, again.  I did not give it to her... Now these are the symptoms I'm dealing with.  She gets red in various places.  She got red around the sides of her butt, it was as red as a coke can!  I gave her a bath, and the next day that area was pink.  She gets the redness on her belly, I put alcohol on it with a washcloth, and within a few hours it's not as red, apply the alcohol a few times, it goes away.  Ears, they were as red as a coke can today, put alcohol on a washcloth, rubbed the inside of her ears, within two hours half of the redness went away completely, and some parts are now only light pink.  Could this be an allergy?  Over $500 in vet bills, and I don't want to keep her on antibotics so much, and no answers.  She also got crusty drandruff on top of dandruff on top of her head, what is that?  Could she possibly be allergic to my cat?  My boyfriend and I were fine with the cat for the first 2 1/2 years of the cats' life, and all of a sudden, we are both allergic to her.  The vet laughed at me when I asked him if the dog could be allergic to the cat.  I don't know, at this point.  I desperately seek for answers.
  Thank you.

Answer
What are you feeding her?  Most of her calories should be coming from a commercial dog chow.  Most dogs will thrive on most brands.

I am a little confused.  She seems to be responding to both the allergy medicine and antibiotics.  The alcohol should irritate skin reddened by allergies, not heal it.  I tend to go along with the first vet and reduce the baths.  But the baths seem to be helping?  You may need to pay for allergy testing and identify specifically what she is allergic to if anything.