Can the owner of a S-Corp who currently pays her children (under age 18) as employees include them in the Simple 401k?

Yes, but keep in mind that the qualification of the plan may depend on the true nature of the relationship as employer/employee. If the W-2 compensation is reasonable, there should be no problem. Banks, but not all financial institutions will permit the establishment of an account for a minor because of "recission" issues (which don't generally occur in FDIC insured accounts, and so on).