The short answer is that you can't prevent your children's father from obtaining custody if something happens to you.
California law has very clearly defined rules for determining who gets the children after a parent passes away. Under Probate Code Section 1500, a parent may nominate a guardian at any time and may make that nomination contingent upon some future occurrence – such as the parent’s death.
However, the nomination of a guardian requires the written consent of the other parent unless that parent is also deceased or has had his or her parental rights terminated. In this case, the father is certainly living. And, contrary to the misinformation on some of the television shows, her parental rights have not been terminated by a court. (You can’t give up parental rights without court approval.)
In short, the father would have to consent to the nomination of your parents. That’s what Probate Code Section 1500(a) says.
And, there is a bigger problem. Probate Code Section 1514(a) requires that the court find that the appointment of a guardian is necessary or convenient before even considering an application for guardianship. The “convenience” test applies primarily when the guardianship is established to manage money. When the issue is the care of the children (and not just money) the question is whether a guardian is necessary.
On that point, California law hasn’t changed in 100 years. When there is a living parent, the appointment of a guardian isn’t necessary. When a guardian isn’t necessary, the court can’t even CONSIDER nominations. If the court can’t consider nominations, then it never gets to the issue of the best interests of the child.
There are three exceptions. One, if it can be proven that the father truly abandoned the child. That doesn't mean he isn't a large part of her life. It means that he has disappeared from her life entirely. Two, if it can be shown that living with the father would be actually harmful to your daughter, then that could be a basis for triggering a guardianship.
But, asking your parents to prove that the father would be harmful to your daughter is basically asking them to bring an action to terminate his parental rights. The big question there is, if the father was so dangerous, why didn't the mother seek to terminate rights while she was alive?
That brings up the third option. Bring an action to terminate parental rights now.
The question you didn't ask, but I think might be important here, is whether your parents would have visitation rights even if the father got custody. In that case, they would probably be able to get visitation. You might want to meet with a lawyer in your area to discuss your options and your parents' options.