You are not a citizen until you are sworn in. If you are denied because of failure to pass the English or the civics test, you will be automatically rescheduled within 90 days. If you are not approved for some other reason, you may be given time to overcome the problem.
For 2009, the American Opportunity Credit--which is a variation of the Hope Credit--will be allowed for 4 years. For years before and after the new credit is allowed, the Hope credit is supposed to be for 2 years.
So, if your child earned less than four years of college credit as of January 1, 2014, you can claim the credit on your 2014 return. Note: You can only claim the credit for a year during which the student carries at least a half-time course load for a minimum of one semester beginning in that year.