Between marriages, migrations, the wars, and the privacy act that's so prevalent now, it's hard to trace people in the more modern decades - especially women.
The name Villett is also a little tricky to trace - it seems to be related to 3 or 4 different origins - French Canada, English Canada, France, Italy, etc., so there are potentially at least a dozen different ways to spell it. If the individual became creative in the way he spelled his name to make himself stand out, or the enumerator decided to spell it the way he thought it was pronounced, the variations could be endless. Since George E Villett is listed as a Canadian in the 1920 census, it's possible he and Kate came directly to California from Canada after the 1910 census was done, which could explain why he wasn't found in 1910.

The 1940 census won't become available to researchers until about 2012. By law, it is released 72 years from the date of enumeration to make sure that anyone who was on it will be either gone or too old to care if someone sees their name on a document showing where they lived 7 decades earlier.

For almost any other type of research, one almost has to go to the place where the person was known to have lived and do a manual search of the records. To hire it done tends to be quite expensive. If you're up for doing microfilm research, you could order microfilm of the area newspapers to see if you can spot her name, but if she was employed as a domestic, it's doubtful she would have been mentioned except for a marriage or death. I personally try to avoid microfilm readers because I tend to get migraines from the movement on the screen.

If you know anyone who knew her, you could have a sit-down with them and see what they remember about where she was, what she was doing, and who she associated with. That could help you pinpoint her whereabouts later on and make finding her a little easier.
I hope you find what you're looking for. Persistence pays off, if you can manage to deal with the frustration. Good luck.