The long and short of it: I hope you live in OC. Orange County excuses anyone who is a primary caregiver. That's it. You don't have to serve.
But if you live in LA County, it's not as easy. First of all, if your child is 5 and under, you can be excused. Just say you are the full-time caregiver of a child under 5. All done.
Unfortunately, if your child(ren) is(are) school-age, we don't have an automatic excuse. The most that can be done is to get an extension to a more convenient time when you can arrange daycare. (An isolated incident: when I was working, I went down to the courthouse and was going to ask for an extension. As soon as I said, I couldn't arrange daycare that week, the clerk excused me completely. This was in Long Beach and at the discretion of the clerk.)
So what happens with the rest of us homeschoolers?
1) You can roll the dice and hope you don't get picked the first day. In LA, if you are not assigned to a court the first day, you are excused from further service that year.
2) Hope that you can call in each day to see if you have to report. Perhaps they won't need you at all for the week you call in and then you're done.
3) You can plead your case to a clerk. I wonder what they say if you can't afford day care? Also, I think they are trained to ignore the words homeschooling. They figure that all kids need a break from schooling, so they assume you can come during a school break.
4) If you are called into a courtroom, you can tell the judge that service is a hardship. I've seen judges be VERY lenient in who they let go. At this point, you can say you homeschool and can't afford day care, etc.
5) Finally, start a business quick! I found that court personnel respond favorably if jury service would be a financial hardship. When you arrive at the jury room, you fill out a form. They go through a list and say that if your employer pays for jury service, write in the number of days. If you own a business or your employer does not pay, enter 0. Do you know what the number is for retired folks and stay-at-home parents? 99 They assume you can serve indefinitely!
6) Schedule your jury service around the end-of-year holidays. They can't start a case if the judge or one of the lawyers is on vacation.
Even though we are not off the hook for jury service in LA, there is a good chance you won't have to serve at all. Good luck!