Most U.S. citizens residing any place in the world have to file U.S. tax returns. U.S citizens residing in Israel with U.S. children with social security numbers can potentially be eligible for refundable credits. To be eligible, the tax payer must have earned income such as salary or business income.
The rules regarding tax return preparation are complex and a professional in the field should be well informed in order to prepare these types of tax returns.
Increased IRS scrutiny of foreign returns highlights the need for professional competent tax advice. Proper documentation of all sources of income and expense is crucial and documents need to be maintained for seven years.
The following link may be of use to someone new to tax filings.