How do I change the beneficiaries on my life insurance policy to include my children's children in the event of my child is dead?

Essentially what you need to do is to designate your grandchildren as "contingent beneficiaries" of the insurance policy. Assuming that your child(ren) is now the only person(s) designated as the beneficiary(ies), you would need to contact the agent who sold you the policy, or the insurer itself, and request the proper form by which to add the contingent beneficiary. You would then return the completed and signed document to the agent or the insurer, as directed.

A potential complication exists if your grandchildren are minors at the time of your death and your children have predeceased you. The problem is that the insurer will generally be unwilling to pay the proceeds directly to a minor, even if he/she/they are the designated contingent beneficiaries. Therefore, you should think through whom you wish to designate the recipient of the proceeds on behalf of the minors and designate that person/persons/institution as the recipient of the policy proceeds.

You can also consider the establishment of a trust to serve that purpose, but you will want to get legal advice to do that.