If she wants to dissolve the marriage, she can do so, whether or not you "sign the papers". The grounds for dissolution in California is "irreconcilable differences", and if she testifies there are irreconcilable differences, the fact that you disagree with her doesn't stop her.
You should spend some time to figuring out the best arrangement for parenting your kids, even if you are divorced.
There is a big misconception with "sign the papers" in dissolutions of marriage. If your wife files a petition for dissolution and you are served with the summons and petition, she can proceed with default if you don't do anything. You should consult a family law attorney in your area and start working on a child sharing and co-parenting plan.
Disclaimer: The preceding is not intended as legal advice and does not create an attorney clinet relatioship.
Practically speaking, what do you think refusing to sign will do? Will it make your wife give up on the divorce? Do you think it will make you look like the better parent and her the worst? Kids have a funny way of processing information. So, who knows what they will think? One thing is certain, they will feel the stress you are both under; they will internalize it; they will start acting out. Are you doing this for you or for your kids? If you're sure you're doing this for your kids, how do they benefit? I'm no therapist, and I don't pretend to be. I've learned a lot from working with them and from training in divorce and high conflict divorce by and with therapists. My thoughts on your question: you're doing this for you. This is something over which you do not have control. The court will give her the divorce whether you "sign the papers" or not. Perhaps you energy and drive would be better used on controlling what you can: being a good father to your children, making sure they are always happy when they are with you, making sure their needs are met, letting them know that no matter what happens, you will always love them and be there for them. Life is way too short for this. Accept what you cannot control, and focus on what you can. You're kids will thank you, and you will be much more at peace. It's not easy, but with practice, it can be achieved.
For more information on consensual divorce resolutions ("CDR"), feel free to visit my web site.
Ultimately if your wife wants the divorce, she will get the divorce. Either with your cooperation or without.
Having said that, I have had several clients in the past few years who prepared and filed a Response to the divorce action and did not request a divorce themselves, but included a statement that they thought the marriage was worth fighting for and were willing to attend counseling, classes, or whatever it took to try and repair the rift. Not for any legal purpose, but to send a message to the spouse that maybe divorce isn't the only option.
So far, of five clients who have done this, 2 couples are still together now. I'm not saying this will work for you, but you could consider the option.