Here is a link to the California Franchise Tax Board (FTB) publication that describes what determines whether you are a California resident for income tax purposes.
FTB Publication 1031, Guidelines for Determining Resident Status
One of the things that is discussed in the publication is the concept of domicile, which is different from residence. In most cases, if your domicile is in California you will be considered a California resident, even if you don't spend a lot of time there during the year. The California FTB is very aggressive about treating people as California residents. With your family in California, you would have a hard time convincing them that California is not your domicile.
If you are considered a California resident, all of your income is subject to California tax, no matter where the income is from. If you worked in a state that has income tax, there would be some allocation of tax between the two states based on how many days you worked in each state. But since Washington has no income tax, as a California resident you would simply pay California tax on all your income, and it wouldn't matter how much of the income is earned in California and how much is earned in Washington.
