Can minors be part of corporation?
From your question I understand that you would like to list your children as official shareholders of your corporation. I believe each state might have specific laws about that, so I will only give you an example of Delaware corporation (for your specific state I recommend consulting a business attorney licensed in your state):
According to the Delaware Dept. Of State they do not look at age. Delaware business law is silent on this point, so here's the general thinking: Shares are considered to be personal property (anything other than real estate is personal property). Minors can hold title in personal property, but if a formal transfer of title is required which would require the minor to execute a contract then the minor would not be able to do that. The minor would have to be represented by a parent/attorney/custodian/guardian.
Another way would be to hold the shares in a trust in the name of the minor but managed by an adult.
Hope that helps.