Cephlasporins are not very good for staph, skin or structure......you need a macrolide or erythromycin type antibiotic.....sounds like your current Vet does not know a lot about antibiotics.....
I am sorry your Yorkie is going thru this.....and when they are on antibiotics for a long time then they get diahhea ....because you are killing the good bacteria too....
Good luck...