From CA vehicle code and Caltrans updated June of 2014:
"In summary, nonresidents may tow two trailers with a non-commercial license IF their base state allows it. However, they would still need a valid medical certificate per 12502 CVC."
Looks like they have added the need for a medical certificate which you will have to research. I don't know if it is the full on Doctor's certificate or the self evaluation.
Take the following for what its worth, free. This is just my opinion based on my experiences.
CA did change and eliminate much of their recreational doubles towing language with the enforcement of the non-commercial class A. This enforcement was mainly due to big, heavy, triple axel trailers. The new language is left to interpretation. In my experiences it was interpreted to be legal based on the definition of a "passenger car" and a "motor truck". Look up CVC 21715(a) and subsections 465, 362, and 410 and you can decide for yourself.