Re: Moisture under stucco.
The paint could be acting as a vapor barrier and holding moisture in. Stucco shouldn't be painted. When it is, a special latex based elastomeric should be used, although a good latex applied properly can breath OK, but could still cause problems. IF painted with an oil based paint, that's a possible source of the problem.
That being said, our stucco is painted and has been for 10 years and seem OK. IT's original to the home and 86 years old.
Another problem could be too much shade and not enouhg sun exposure to heat it up.
Finally, has any insulation been added to the home? Retrofitting insulation cna cause moisture issues.
1925 Two-Story Stucco Beaux Arts Neoclassical