How old are your kids? If your kids are really young you're probably better off using the college money on yourself. The increase in income you'll have as a college graduate early on in their lives will have more of an impact I think. You can always start a college fund for them when you start working. You should avoid taking on student loans at all costs. It wont make much sense for you to save this GI Bill for your kids if it means having to bear the burden of student debt. Those student debt payments could be the difference between being able to afford rent in a neighborhood with a great school district and one that's not.
The other reason I strongly suggest you use the GI BILL on yourself is that the BAH they give you will help you pay bills in addition to going to school. Depending on your major you will very likely want to do internships. I over valued my military experience and didn't do internships and that was a huge mistake. Internships, especially for the corporate sector, are HUGE. The thing is a lot of these internships are unpaid so you will need a source of income.
Now, the GI BIll is not all or nothing. What you might want to consider is using it to get yourself started in school and then once you have scholarships and a feel for how much work and school you can handle you can stop using your GI Bill. The way it works is you have to reapply every semester through the college so you can just stop using it whenever you like.
Having said that, if you really don't want to use the GI Bill on yourself
then at least you're in the right state. California Community Colleges are pretty cheap compared to most other places so its doable to put yourself through Community College at least. If you're not already familiar, assist.org is a website that lists the transfer agreements for all community colleges in california and the UC and CSU systems.
I think a big part of the decision here is for you to realistically assess your ability to both work and do well enough in school to earn scholarships. I knew I couldn't do both. I have no idea how I would do it with kids.
Hit me up. I used the GI bill here in California, went to Community College then transferred to UC Berkeley to a great business program.