Children of Substance Abusers Amendments Act - Title I: Services for Children of Substance Abusers - Amends the Public Health Service Act to direct the Secretary of Health and Human Services, through the Administrator of the Health Resources and Services Administration, to make grants for the Federal share of the cost of community outreach services and services for children of substance abusers. Sets forth program requirements, including providing comprehensive services for the entire family.

Sets forth requirements regarding: (1) the distribution of grants among specified types of entities; and (2) information and assurances which must be included in grant applications. Sets the Federal share at 90 percent. Authorizes appropriations.

Provides for grants for the training of professionals and other staff who provide services to, or come in contact with, children and families of substance abusers. Requires the Administrator to identify the training needs of such professionals and other staff and develop a strategy for satisfying the needs. Prescribes the uses of the grant funds. Authorizes appropriations.

Title II: Home-Visiting Services for At-Risk Families - Directs the Secretary to make competitive three- to five-year grants for the Federal share of the costs of home visiting services, including help in obtaining health and social services. Sets forth priorities in awarding grants and information and assurances which must be included in grant applications. Sets the Federal share at 90 percent. Authorizes appropriations.