KJD22,
Your mother absolutely is eligible for the credit. No ifs ands or buts!
The Homestead property tax exemption, i.e. one of the two reasons a senior citizen would not qualify for that credit, is only available to senior citizen homeowners who have lived in their home for 10 years or more and have applied for the exemption with their county tax assessor's office. The application form with all the fine print is at Homestead Exemption Application .
The other exception to not qualifying is having the Disabled Veteran Exemption (also mentioned in that above application though applied for differently.) The disability must have been service related.
