I do not think it makes a difference if you aren't getting cash aid for yourself. You are still responsible for your children's housing. Therefore you should be eligible to receive a voucher for help with moving costs. This takes approximately 2 weeks and sometimes even 3 to get a call back from the assistance places. I myself tried to get a voucher for help with my rental deposit. They gave me the run around for an entire week (approx. 4 different agencies ). They told me since I was moving to alameda county that I had to contact alameda county agencies. Then when I called the Alameda county agencies they told me since I lived in Contra Costa County that I needed to get into contact with Contra costa counties.
I however was NOT enrolled in Cal Works at the time. And I know that you get way more assistance if you are in Cal works. Even if it is just for your children, you should definitely be able to get assistance, ESPECIALLY because there are children involved.
Call 211 from any phone. They will ask you what county you are in. They can give you agencies. The only thing is, if you are enrolled in calworks, they want you to go through your worker. But get on it ASAP because it does take some time and you don't want to be living in a motel with no where to put your stuff because this WILL and does happen because of the time sensetive assistance you are asking for.
having gone through the moving assistance from 211 just recently. http://211.org/